WORST_CASE(?,O(1))
proof of input_tYJx5FecqC.trs
# AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished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)


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(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
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(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'))




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(2)
BOUNDS(1, 1)