WORST_CASE(Omega(n^1),O(n^2))
proof of /export/starexec/sandbox/benchmark/theBenchmark.trs
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 486 ms]
(2) CpxRelTRS
(3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) CpxWeightedTrs
    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxTypedWeightedTrs
    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (12) CpxRNTS
    (13) InliningProof [UPPER BOUND(ID), 443 ms]
    (14) CpxRNTS
    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRNTS
    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 139 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 245 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 117 ms]
    (30) CpxRNTS
    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 141 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
    (36) CpxRNTS
    (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 371 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 135 ms]
    (42) CpxRNTS
    (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 3366 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 2225 ms]
    (48) CpxRNTS
    (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (50) CpxRNTS
    (51) IntTrsBoundProof [UPPER BOUND(ID), 1831 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 559 ms]
    (54) CpxRNTS
    (55) FinalProof [FINISHED, 0 ms]
    (56) BOUNDS(1, n^2)
(57) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(58) TRS for Loop Detection
    (59) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
    (60) BEST
        (61) proven lower bound
            (62) LowerBoundPropagationProof [FINISHED, 0 ms]
            (63) BOUNDS(n^1, INF)
        (64) TRS for Loop Detection


----------------------------------------

(0)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   COND(true, z0, z1) -> c(COND(gr(z0, z1), p(z0), z1), GR(z0, z1))
   COND(true, z0, z1) -> c1(COND(gr(z0, z1), p(z0), z1), P(z0))
   GR(0, z0) -> c2
   GR(s(z0), 0) -> c3
   GR(s(z0), s(z1)) -> c4(GR(z0, z1))
   P(0) -> c5
   P(s(z0)) -> c6

The (relative) TRS S consists of the following rules:

   cond(true, z0, z1) -> cond(gr(z0, z1), p(z0), z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
----------------------------------------

(1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   COND(true, z0, z1) -> c(COND(gr(z0, z1), p(z0), z1), GR(z0, z1))
   COND(true, z0, z1) -> c1(COND(gr(z0, z1), p(z0), z1), P(z0))
   GR(0, z0) -> c2
   GR(s(z0), 0) -> c3
   GR(s(z0), s(z1)) -> c4(GR(z0, z1))
   P(0) -> c5
   P(s(z0)) -> c6

The (relative) TRS S consists of the following rules:

   cond(true, z0, z1) -> cond(gr(z0, z1), p(z0), z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
----------------------------------------

(3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   COND(true, z0, z1) -> c(COND(gr(z0, z1), p(z0), z1), GR(z0, z1)) [1]
   COND(true, z0, z1) -> c1(COND(gr(z0, z1), p(z0), z1), P(z0)) [1]
   GR(0, z0) -> c2 [1]
   GR(s(z0), 0) -> c3 [1]
   GR(s(z0), s(z1)) -> c4(GR(z0, z1)) [1]
   P(0) -> c5 [1]
   P(s(z0)) -> c6 [1]
   cond(true, z0, z1) -> cond(gr(z0, z1), p(z0), z1) [0]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   gr(s(z0), s(z1)) -> gr(z0, z1) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(5) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(6)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   COND(true, z0, z1) -> c(COND(gr(z0, z1), p(z0), z1), GR(z0, z1)) [1]
   COND(true, z0, z1) -> c1(COND(gr(z0, z1), p(z0), z1), P(z0)) [1]
   GR(0, z0) -> c2 [1]
   GR(s(z0), 0) -> c3 [1]
   GR(s(z0), s(z1)) -> c4(GR(z0, z1)) [1]
   P(0) -> c5 [1]
   P(s(z0)) -> c6 [1]
   cond(true, z0, z1) -> cond(gr(z0, z1), p(z0), z1) [0]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   gr(s(z0), s(z1)) -> gr(z0, z1) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]

The TRS has the following type information:
COND :: true:false -> 0:s -> 0:s -> c:c1
true :: true:false
c :: c:c1 -> c2:c3:c4 -> c:c1
gr :: 0:s -> 0:s -> true:false
p :: 0:s -> 0:s
GR :: 0:s -> 0:s -> c2:c3:c4
c1 :: c:c1 -> c5:c6 -> c:c1
P :: 0:s -> c5:c6
0 :: 0:s
c2 :: c2:c3:c4
s :: 0:s -> 0:s
c3 :: c2:c3:c4
c4 :: c2:c3:c4 -> c2:c3:c4
c5 :: c5:c6
c6 :: c5:c6
cond :: true:false -> 0:s -> 0:s -> cond
false :: true:false

Rewrite Strategy: INNERMOST
----------------------------------------

(7) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   COND_3
   GR_2
   P_1

(c) The following functions are completely defined:

   cond_3
   gr_2
   p_1

Due to the following rules being added:

   cond(v0, v1, v2) -> const1 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

And the following fresh constants:    const1, null_gr, const

----------------------------------------

(8)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   COND(true, z0, z1) -> c(COND(gr(z0, z1), p(z0), z1), GR(z0, z1)) [1]
   COND(true, z0, z1) -> c1(COND(gr(z0, z1), p(z0), z1), P(z0)) [1]
   GR(0, z0) -> c2 [1]
   GR(s(z0), 0) -> c3 [1]
   GR(s(z0), s(z1)) -> c4(GR(z0, z1)) [1]
   P(0) -> c5 [1]
   P(s(z0)) -> c6 [1]
   cond(true, z0, z1) -> cond(gr(z0, z1), p(z0), z1) [0]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   gr(s(z0), s(z1)) -> gr(z0, z1) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]
   cond(v0, v1, v2) -> const1 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

The TRS has the following type information:
COND :: true:false:null_gr -> 0:s -> 0:s -> c:c1
true :: true:false:null_gr
c :: c:c1 -> c2:c3:c4 -> c:c1
gr :: 0:s -> 0:s -> true:false:null_gr
p :: 0:s -> 0:s
GR :: 0:s -> 0:s -> c2:c3:c4
c1 :: c:c1 -> c5:c6 -> c:c1
P :: 0:s -> c5:c6
0 :: 0:s
c2 :: c2:c3:c4
s :: 0:s -> 0:s
c3 :: c2:c3:c4
c4 :: c2:c3:c4 -> c2:c3:c4
c5 :: c5:c6
c6 :: c5:c6
cond :: true:false:null_gr -> 0:s -> 0:s -> const1
false :: true:false:null_gr
const1 :: const1
null_gr :: true:false:null_gr
const :: c:c1

Rewrite Strategy: INNERMOST
----------------------------------------

(9) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(10)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   COND(true, 0, z1) -> c(COND(false, 0, z1), GR(0, z1)) [1]
   COND(true, 0, z1) -> c(COND(false, 0, z1), GR(0, z1)) [1]
   COND(true, s(z0'), 0) -> c(COND(true, z0', 0), GR(s(z0'), 0)) [1]
   COND(true, s(z0'), 0) -> c(COND(true, 0, 0), GR(s(z0'), 0)) [1]
   COND(true, s(z0''), s(z1')) -> c(COND(gr(z0'', z1'), z0'', s(z1')), GR(s(z0''), s(z1'))) [1]
   COND(true, s(z0''), s(z1')) -> c(COND(gr(z0'', z1'), 0, s(z1')), GR(s(z0''), s(z1'))) [1]
   COND(true, 0, z1) -> c(COND(null_gr, 0, z1), GR(0, z1)) [1]
   COND(true, s(z01), z1) -> c(COND(null_gr, z01, z1), GR(s(z01), z1)) [1]
   COND(true, z0, z1) -> c(COND(null_gr, 0, z1), GR(z0, z1)) [1]
   COND(true, 0, z1) -> c1(COND(false, 0, z1), P(0)) [1]
   COND(true, 0, z1) -> c1(COND(false, 0, z1), P(0)) [1]
   COND(true, s(z02), 0) -> c1(COND(true, z02, 0), P(s(z02))) [1]
   COND(true, s(z02), 0) -> c1(COND(true, 0, 0), P(s(z02))) [1]
   COND(true, s(z03), s(z1'')) -> c1(COND(gr(z03, z1''), z03, s(z1'')), P(s(z03))) [1]
   COND(true, s(z03), s(z1'')) -> c1(COND(gr(z03, z1''), 0, s(z1'')), P(s(z03))) [1]
   COND(true, 0, z1) -> c1(COND(null_gr, 0, z1), P(0)) [1]
   COND(true, s(z04), z1) -> c1(COND(null_gr, z04, z1), P(s(z04))) [1]
   COND(true, z0, z1) -> c1(COND(null_gr, 0, z1), P(z0)) [1]
   GR(0, z0) -> c2 [1]
   GR(s(z0), 0) -> c3 [1]
   GR(s(z0), s(z1)) -> c4(GR(z0, z1)) [1]
   P(0) -> c5 [1]
   P(s(z0)) -> c6 [1]
   cond(true, 0, z1) -> cond(false, 0, z1) [0]
   cond(true, 0, z1) -> cond(false, 0, z1) [0]
   cond(true, s(z05), 0) -> cond(true, z05, 0) [0]
   cond(true, s(z05), 0) -> cond(true, 0, 0) [0]
   cond(true, s(z06), s(z11)) -> cond(gr(z06, z11), z06, s(z11)) [0]
   cond(true, s(z06), s(z11)) -> cond(gr(z06, z11), 0, s(z11)) [0]
   cond(true, 0, z1) -> cond(null_gr, 0, z1) [0]
   cond(true, s(z07), z1) -> cond(null_gr, z07, z1) [0]
   cond(true, z0, z1) -> cond(null_gr, 0, z1) [0]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   gr(s(z0), s(z1)) -> gr(z0, z1) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]
   cond(v0, v1, v2) -> const1 [0]
   gr(v0, v1) -> null_gr [0]
   p(v0) -> 0 [0]

The TRS has the following type information:
COND :: true:false:null_gr -> 0:s -> 0:s -> c:c1
true :: true:false:null_gr
c :: c:c1 -> c2:c3:c4 -> c:c1
gr :: 0:s -> 0:s -> true:false:null_gr
p :: 0:s -> 0:s
GR :: 0:s -> 0:s -> c2:c3:c4
c1 :: c:c1 -> c5:c6 -> c:c1
P :: 0:s -> c5:c6
0 :: 0:s
c2 :: c2:c3:c4
s :: 0:s -> 0:s
c3 :: c2:c3:c4
c4 :: c2:c3:c4 -> c2:c3:c4
c5 :: c5:c6
c6 :: c5:c6
cond :: true:false:null_gr -> 0:s -> 0:s -> const1
false :: true:false:null_gr
const1 :: const1
null_gr :: true:false:null_gr
const :: c:c1

Rewrite Strategy: INNERMOST
----------------------------------------

(11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   true => 2
   0 => 0
   c2 => 0
   c3 => 1
   c5 => 0
   c6 => 1
   false => 1
   const1 => 0
   null_gr => 0
   const => 0

----------------------------------------

(12)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z0'', z1'), z0'', 1 + z1') + GR(1 + z0'', 1 + z1') :|: z = 2, z'' = 1 + z1', z1' >= 0, z' = 1 + z0'', z0'' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z0'', z1'), 0, 1 + z1') + GR(1 + z0'', 1 + z1') :|: z = 2, z'' = 1 + z1', z1' >= 0, z' = 1 + z0'', z0'' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z03, z1''), z03, 1 + z1'') + P(1 + z03) :|: z = 2, z'' = 1 + z1'', z' = 1 + z03, z03 >= 0, z1'' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z03, z1''), 0, 1 + z1'') + P(1 + z03) :|: z = 2, z'' = 1 + z1'', z' = 1 + z03, z03 >= 0, z1'' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z0', 0) + GR(1 + z0', 0) :|: z = 2, z'' = 0, z0' >= 0, z' = 1 + z0'
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z02, 0) + P(1 + z02) :|: z = 2, z'' = 0, z02 >= 0, z' = 1 + z02
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + P(1 + z02) :|: z = 2, z'' = 0, z02 >= 0, z' = 1 + z02
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + z0', 0) :|: z = 2, z'' = 0, z0' >= 0, z' = 1 + z0'
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z1) + P(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z1) + GR(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z01, z1) + GR(1 + z01, z1) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z04, z1) + P(1 + z04) :|: z = 2, z04 >= 0, z1 >= 0, z' = 1 + z04, z'' = z1
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z1) + P(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z1) + P(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z1) + GR(z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z1) + GR(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   GR(z, z') -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z0 >= 0, z = 0, z' = z0
   GR(z, z') -{ 1 }-> 1 + GR(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   P(z) -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z06, z11), z06, 1 + z11) :|: z = 2, z11 >= 0, z06 >= 0, z' = 1 + z06, z'' = 1 + z11
   cond(z, z', z'') -{ 0 }-> cond(gr(z06, z11), 0, 1 + z11) :|: z = 2, z11 >= 0, z06 >= 0, z' = 1 + z06, z'' = 1 + z11
   cond(z, z', z'') -{ 0 }-> cond(2, z05, 0) :|: z = 2, z'' = 0, z05 >= 0, z' = 1 + z05
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z05 >= 0, z' = 1 + z05
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   cond(z, z', z'') -{ 0 }-> cond(0, z07, z1) :|: z = 2, z1 >= 0, z07 >= 0, z' = 1 + z07, z'' = z1
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   gr(z, z') -{ 0 }-> gr(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   gr(z, z') -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   p(z) -{ 0 }-> z0 :|: z = 1 + z0, z0 >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


----------------------------------------

(13) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   P(z) -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0

----------------------------------------

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z0'', z1'), z0'', 1 + z1') + GR(1 + z0'', 1 + z1') :|: z = 2, z'' = 1 + z1', z1' >= 0, z' = 1 + z0'', z0'' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z0'', z1'), 0, 1 + z1') + GR(1 + z0'', 1 + z1') :|: z = 2, z'' = 1 + z1', z1' >= 0, z' = 1 + z0'', z0'' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z03, z1''), z03, 1 + z1'') + 1 :|: z = 2, z'' = 1 + z1'', z' = 1 + z03, z03 >= 0, z1'' >= 0, 1 + z03 = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z03, z1''), 0, 1 + z1'') + 1 :|: z = 2, z'' = 1 + z1'', z' = 1 + z03, z03 >= 0, z1'' >= 0, 1 + z03 = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z0', 0) + GR(1 + z0', 0) :|: z = 2, z'' = 0, z0' >= 0, z' = 1 + z0'
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z02, 0) + 1 :|: z = 2, z'' = 0, z02 >= 0, z' = 1 + z02, 1 + z02 = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + z0', 0) :|: z = 2, z'' = 0, z0' >= 0, z' = 1 + z0'
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z02 >= 0, z' = 1 + z02, 1 + z02 = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z1) + GR(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z1) + 0 :|: z = 2, z1 >= 0, z' = 0, z'' = z1, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z01, z1) + GR(1 + z01, z1) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z04, z1) + 1 :|: z = 2, z04 >= 0, z1 >= 0, z' = 1 + z04, z'' = z1, 1 + z04 = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z1) + GR(z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z1) + GR(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z1) + 1 :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, z0 = 1 + z0', z0' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z1) + 0 :|: z = 2, z1 >= 0, z' = 0, z'' = z1, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z1) + 0 :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, z0 = 0
   GR(z, z') -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z0 >= 0, z = 0, z' = z0
   GR(z, z') -{ 1 }-> 1 + GR(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   P(z) -{ 1 }-> 1 :|: z = 1 + z0, z0 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z06, z11), z06, 1 + z11) :|: z = 2, z11 >= 0, z06 >= 0, z' = 1 + z06, z'' = 1 + z11
   cond(z, z', z'') -{ 0 }-> cond(gr(z06, z11), 0, 1 + z11) :|: z = 2, z11 >= 0, z06 >= 0, z' = 1 + z06, z'' = 1 + z11
   cond(z, z', z'') -{ 0 }-> cond(2, z05, 0) :|: z = 2, z'' = 0, z05 >= 0, z' = 1 + z05
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z05 >= 0, z' = 1 + z05
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   cond(z, z', z'') -{ 0 }-> cond(0, z07, z1) :|: z = 2, z1 >= 0, z07 >= 0, z' = 1 + z07, z'' = z1
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   gr(z, z') -{ 0 }-> gr(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   gr(z, z') -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   p(z) -{ 0 }-> z0 :|: z = 1 + z0, z0 >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


----------------------------------------

(15) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z' - 1, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z' - 1, z'') + GR(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0


----------------------------------------

(17) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { P }
   { GR }
   { p }
   { gr }
   { COND }
   { cond }

----------------------------------------

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z' - 1, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z' - 1, z'') + GR(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {P}, {GR}, {p}, {gr}, {COND}, {cond}

----------------------------------------

(19) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z' - 1, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z' - 1, z'') + GR(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {P}, {GR}, {p}, {gr}, {COND}, {cond}

----------------------------------------

(21) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: P
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z' - 1, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z' - 1, z'') + GR(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {P}, {GR}, {p}, {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: ?, size: O(1) [1]

----------------------------------------

(23) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: P
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z' - 1, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z' - 1, z'') + GR(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {p}, {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]

----------------------------------------

(25) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z' - 1, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z' - 1, z'') + GR(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {p}, {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]

----------------------------------------

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: GR
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

----------------------------------------

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z' - 1, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z' - 1, z'') + GR(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {p}, {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: ?, size: O(n^1) [z]

----------------------------------------

(29) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: GR
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z'

----------------------------------------

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + GR(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, 0, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(2, z' - 1, 0) + GR(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(1, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, 0, z'') + GR(0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 1 }-> 1 + COND(0, z' - 1, z'') + GR(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]

----------------------------------------

(31) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + s2 :|: s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + s1 :|: s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]

----------------------------------------

(33) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

----------------------------------------

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + s2 :|: s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + s1 :|: s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: ?, size: O(n^1) [z]

----------------------------------------

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + s2 :|: s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + s1 :|: s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]

----------------------------------------

(37) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + s2 :|: s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + s1 :|: s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]

----------------------------------------

(39) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: gr
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

----------------------------------------

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + s2 :|: s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + s1 :|: s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: ?, size: O(1) [2]

----------------------------------------

(41) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: gr
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + s2 :|: s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + s1 :|: s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) + 1 :|: z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), 0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(gr(z' - 1, z'' - 1), z' - 1, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> gr(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]

----------------------------------------

(43) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 2 }-> 1 + COND(s12, z' - 1, 1 + (z'' - 1)) + 1 :|: s12 >= 0, s12 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(s13, 0, 1 + (z'' - 1)) + 1 :|: s13 >= 0, s13 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(s7, z' - 1, 1 + (z'' - 1)) + s1 :|: s7 >= 0, s7 <= 2, s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(s8, 0, 1 + (z'' - 1)) + s2 :|: s8 >= 0, s8 <= 2, s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(s10, 0, 1 + (z'' - 1)) :|: s10 >= 0, s10 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(s9, z' - 1, 1 + (z'' - 1)) :|: s9 >= 0, s9 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> s11 :|: s11 >= 0, s11 <= 2, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]

----------------------------------------

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: COND
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 2 }-> 1 + COND(s12, z' - 1, 1 + (z'' - 1)) + 1 :|: s12 >= 0, s12 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(s13, 0, 1 + (z'' - 1)) + 1 :|: s13 >= 0, s13 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(s7, z' - 1, 1 + (z'' - 1)) + s1 :|: s7 >= 0, s7 <= 2, s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(s8, 0, 1 + (z'' - 1)) + s2 :|: s8 >= 0, s8 <= 2, s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(s10, 0, 1 + (z'' - 1)) :|: s10 >= 0, s10 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(s9, z' - 1, 1 + (z'' - 1)) :|: s9 >= 0, s9 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> s11 :|: s11 >= 0, s11 <= 2, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND}, {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  COND: runtime: ?, size: O(1) [0]

----------------------------------------

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: COND
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 9 + 3*z' + z'*z'' + 3*z''

----------------------------------------

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 2 }-> 1 + COND(s12, z' - 1, 1 + (z'' - 1)) + 1 :|: s12 >= 0, s12 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(s13, 0, 1 + (z'' - 1)) + 1 :|: s13 >= 0, s13 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(s7, z' - 1, 1 + (z'' - 1)) + s1 :|: s7 >= 0, s7 <= 2, s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(s8, 0, 1 + (z'' - 1)) + s2 :|: s8 >= 0, s8 <= 2, s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, 0, 0) + s'' :|: s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, 0, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 }-> 1 + COND(2, z' - 1, 0) + s' :|: s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(2, z' - 1, 0) + 1 :|: z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(1, 0, z'') + s :|: s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(1, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, 0, z'') + s5 :|: s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 1 :|: z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, 0, z'') + 0 :|: z = 2, z'' >= 0, z' >= 0, z' = 0
   COND(z, z', z'') -{ 3 + z'' }-> 1 + COND(0, z' - 1, z'') + s4 :|: s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 2 }-> 1 + COND(0, z' - 1, z'') + 1 :|: z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(s10, 0, 1 + (z'' - 1)) :|: s10 >= 0, s10 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(s9, z' - 1, 1 + (z'' - 1)) :|: s9 >= 0, s9 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> s11 :|: s11 >= 0, s11 <= 2, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  COND: runtime: O(n^2) [9 + 3*z' + z'*z'' + 3*z''], size: O(1) [0]

----------------------------------------

(49) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s14 + s :|: s14 >= 0, s14 <= 0, s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 9 + 3*z' }-> 1 + s15 + s' :|: s15 >= 0, s15 <= 0, s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 }-> 1 + s16 + s'' :|: s16 >= 0, s16 <= 0, s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 9 + 3*z' + z'*z'' + 3*z'' }-> 1 + s17 + s1 :|: s17 >= 0, s17 <= 0, s7 >= 0, s7 <= 2, s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s18 + s2 :|: s18 >= 0, s18 <= 0, s8 >= 0, s8 <= 2, s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s19 + s3 :|: s19 >= 0, s19 <= 0, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 9 + 3*z' + z'*z'' + 3*z'' }-> 1 + s20 + s4 :|: s20 >= 0, s20 <= 0, s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s21 + s5 :|: s21 >= 0, s21 <= 0, s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s22 + 0 :|: s22 >= 0, s22 <= 0, z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 8 + 3*z' }-> 1 + s23 + 1 :|: s23 >= 0, s23 <= 0, z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 }-> 1 + s24 + 1 :|: s24 >= 0, s24 <= 0, z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 8 + 3*z' + z'*z'' + 2*z'' }-> 1 + s25 + 1 :|: s25 >= 0, s25 <= 0, s12 >= 0, s12 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s26 + 1 :|: s26 >= 0, s26 <= 0, s13 >= 0, s13 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s27 + 0 :|: s27 >= 0, s27 <= 0, z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 8 + 3*z' + z'*z'' + 2*z'' }-> 1 + s28 + 1 :|: s28 >= 0, s28 <= 0, z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s29 + 1 :|: s29 >= 0, s29 <= 0, z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0, z = 2, z'' >= 0, z' >= 0, z' = 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(s10, 0, 1 + (z'' - 1)) :|: s10 >= 0, s10 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(s9, z' - 1, 1 + (z'' - 1)) :|: s9 >= 0, s9 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> s11 :|: s11 >= 0, s11 <= 2, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  COND: runtime: O(n^2) [9 + 3*z' + z'*z'' + 3*z''], size: O(1) [0]

----------------------------------------

(51) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: cond
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s14 + s :|: s14 >= 0, s14 <= 0, s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 9 + 3*z' }-> 1 + s15 + s' :|: s15 >= 0, s15 <= 0, s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 }-> 1 + s16 + s'' :|: s16 >= 0, s16 <= 0, s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 9 + 3*z' + z'*z'' + 3*z'' }-> 1 + s17 + s1 :|: s17 >= 0, s17 <= 0, s7 >= 0, s7 <= 2, s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s18 + s2 :|: s18 >= 0, s18 <= 0, s8 >= 0, s8 <= 2, s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s19 + s3 :|: s19 >= 0, s19 <= 0, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 9 + 3*z' + z'*z'' + 3*z'' }-> 1 + s20 + s4 :|: s20 >= 0, s20 <= 0, s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s21 + s5 :|: s21 >= 0, s21 <= 0, s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s22 + 0 :|: s22 >= 0, s22 <= 0, z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 8 + 3*z' }-> 1 + s23 + 1 :|: s23 >= 0, s23 <= 0, z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 }-> 1 + s24 + 1 :|: s24 >= 0, s24 <= 0, z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 8 + 3*z' + z'*z'' + 2*z'' }-> 1 + s25 + 1 :|: s25 >= 0, s25 <= 0, s12 >= 0, s12 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s26 + 1 :|: s26 >= 0, s26 <= 0, s13 >= 0, s13 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s27 + 0 :|: s27 >= 0, s27 <= 0, z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 8 + 3*z' + z'*z'' + 2*z'' }-> 1 + s28 + 1 :|: s28 >= 0, s28 <= 0, z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s29 + 1 :|: s29 >= 0, s29 <= 0, z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0, z = 2, z'' >= 0, z' >= 0, z' = 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(s10, 0, 1 + (z'' - 1)) :|: s10 >= 0, s10 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(s9, z' - 1, 1 + (z'' - 1)) :|: s9 >= 0, s9 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> s11 :|: s11 >= 0, s11 <= 2, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {cond}
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  COND: runtime: O(n^2) [9 + 3*z' + z'*z'' + 3*z''], size: O(1) [0]
  cond: runtime: ?, size: O(1) [0]

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(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: cond
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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(54)
Obligation:
Complexity RNTS consisting of the following rules:

   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s14 + s :|: s14 >= 0, s14 <= 0, s >= 0, s <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 9 + 3*z' }-> 1 + s15 + s' :|: s15 >= 0, s15 <= 0, s' >= 0, s' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 }-> 1 + s16 + s'' :|: s16 >= 0, s16 <= 0, s'' >= 0, s'' <= 1 + (z' - 1), z = 2, z'' = 0, z' - 1 >= 0
   COND(z, z', z'') -{ 9 + 3*z' + z'*z'' + 3*z'' }-> 1 + s17 + s1 :|: s17 >= 0, s17 <= 0, s7 >= 0, s7 <= 2, s1 >= 0, s1 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s18 + s2 :|: s18 >= 0, s18 <= 0, s8 >= 0, s8 <= 2, s2 >= 0, s2 <= 1 + (z' - 1), z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s19 + s3 :|: s19 >= 0, s19 <= 0, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' = 0
   COND(z, z', z'') -{ 9 + 3*z' + z'*z'' + 3*z'' }-> 1 + s20 + s4 :|: s20 >= 0, s20 <= 0, s4 >= 0, s4 <= 1 + (z' - 1), z = 2, z'' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 12 + 4*z'' }-> 1 + s21 + s5 :|: s21 >= 0, s21 <= 0, s5 >= 0, s5 <= z', z = 2, z'' >= 0, z' >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s22 + 0 :|: s22 >= 0, s22 <= 0, z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 8 + 3*z' }-> 1 + s23 + 1 :|: s23 >= 0, s23 <= 0, z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 }-> 1 + s24 + 1 :|: s24 >= 0, s24 <= 0, z = 2, z'' = 0, z' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 8 + 3*z' + z'*z'' + 2*z'' }-> 1 + s25 + 1 :|: s25 >= 0, s25 <= 0, s12 >= 0, s12 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s26 + 1 :|: s26 >= 0, s26 <= 0, s13 >= 0, s13 <= 2, z = 2, z' - 1 >= 0, z'' - 1 >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s27 + 0 :|: s27 >= 0, s27 <= 0, z = 2, z'' >= 0, z' = 0, 0 = 0
   COND(z, z', z'') -{ 8 + 3*z' + z'*z'' + 2*z'' }-> 1 + s28 + 1 :|: s28 >= 0, s28 <= 0, z = 2, z' - 1 >= 0, z'' >= 0, 1 + (z' - 1) = 1 + z0, z0 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s29 + 1 :|: s29 >= 0, s29 <= 0, z = 2, z'' >= 0, z' >= 0, z' - 1 >= 0
   COND(z, z', z'') -{ 11 + 3*z'' }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0, z = 2, z'' >= 0, z' >= 0, z' = 0
   GR(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   GR(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   GR(z, z') -{ 2 + z' }-> 1 + s6 :|: s6 >= 0, s6 <= z - 1, z' - 1 >= 0, z - 1 >= 0
   P(z) -{ 1 }-> 1 :|: z - 1 >= 0
   P(z) -{ 1 }-> 0 :|: z = 0
   cond(z, z', z'') -{ 0 }-> cond(s10, 0, 1 + (z'' - 1)) :|: s10 >= 0, s10 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(s9, z' - 1, 1 + (z'' - 1)) :|: s9 >= 0, s9 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, 0, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(2, z' - 1, 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> cond(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   cond(z, z', z'') -{ 0 }-> cond(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0
   cond(z, z', z'') -{ 0 }-> cond(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   cond(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gr(z, z') -{ 0 }-> s11 :|: s11 >= 0, s11 <= 2, z' - 1 >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  P: runtime: O(1) [1], size: O(1) [1]
  GR: runtime: O(n^1) [2 + z'], size: O(n^1) [z]
  p: runtime: O(1) [0], size: O(n^1) [z]
  gr: runtime: O(1) [0], size: O(1) [2]
  COND: runtime: O(n^2) [9 + 3*z' + z'*z'' + 3*z''], size: O(1) [0]
  cond: runtime: O(1) [0], size: O(1) [0]

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(55) FinalProof (FINISHED)
Computed overall runtime complexity
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(56)
BOUNDS(1, n^2)

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(57) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
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(58)
Obligation:
Analyzing the following TRS for decreasing loops:

The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   COND(true, z0, z1) -> c(COND(gr(z0, z1), p(z0), z1), GR(z0, z1))
   COND(true, z0, z1) -> c1(COND(gr(z0, z1), p(z0), z1), P(z0))
   GR(0, z0) -> c2
   GR(s(z0), 0) -> c3
   GR(s(z0), s(z1)) -> c4(GR(z0, z1))
   P(0) -> c5
   P(s(z0)) -> c6

The (relative) TRS S consists of the following rules:

   cond(true, z0, z1) -> cond(gr(z0, z1), p(z0), z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
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(59) DecreasingLoopProof (LOWER BOUND(ID))
The following loop(s) give(s) rise to the lower bound Omega(n^1):

The rewrite sequence

GR(s(z0), s(z1)) ->^+ c4(GR(z0, z1))

gives rise to a decreasing loop by considering the right hand sides subterm at position [0].

The pumping substitution is [z0 / s(z0), z1 / s(z1)].

The result substitution is [ ].




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(60)
Complex Obligation (BEST)

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(61)
Obligation:
Proved the lower bound n^1 for the following obligation:

The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   COND(true, z0, z1) -> c(COND(gr(z0, z1), p(z0), z1), GR(z0, z1))
   COND(true, z0, z1) -> c1(COND(gr(z0, z1), p(z0), z1), P(z0))
   GR(0, z0) -> c2
   GR(s(z0), 0) -> c3
   GR(s(z0), s(z1)) -> c4(GR(z0, z1))
   P(0) -> c5
   P(s(z0)) -> c6

The (relative) TRS S consists of the following rules:

   cond(true, z0, z1) -> cond(gr(z0, z1), p(z0), z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
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(62) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
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(63)
BOUNDS(n^1, INF)

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(64)
Obligation:
Analyzing the following TRS for decreasing loops:

The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   COND(true, z0, z1) -> c(COND(gr(z0, z1), p(z0), z1), GR(z0, z1))
   COND(true, z0, z1) -> c1(COND(gr(z0, z1), p(z0), z1), P(z0))
   GR(0, z0) -> c2
   GR(s(z0), 0) -> c3
   GR(s(z0), s(z1)) -> c4(GR(z0, z1))
   P(0) -> c5
   P(s(z0)) -> c6

The (relative) TRS S consists of the following rules:

   cond(true, z0, z1) -> cond(gr(z0, z1), p(z0), z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST