WORST_CASE(?,O(1))
proof of input_kt6sC8gTn3.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).

(0) CpxTRS
(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
(2) BOUNDS(1, 1)


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

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).


The TRS R consists of the following rules:

   f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d'))
   f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
Constant runtime complexity proven by termination of constructor-based narrowing.

The maximal most general narrowing sequences give rise to the following rewrite sequences:

f(g(h(a, b), c), d) ->^* if(e, f(.(b, g(h(a, b), c)), d), f(c, d'))

f(g(i(a, b, b'), c), d) ->^* if(e, f(.(b, c), d'), f(.(b', c), d'))




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

(2)
BOUNDS(1, 1)