WORST_CASE(?,O(1))
proof of input_CBZ38xPxvS.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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)


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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:

   gcd(x, 0) -> x
   gcd(0, y) -> y
   gcd(s(x), s(y)) -> if(<(x, y), gcd(s(x), -(y, x)), gcd(-(x, y), s(y)))

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:

gcd(s(x0), s(x1)) ->^* if(<(x0, x1), gcd(s(x0), -(x1, x0)), gcd(-(x0, x1), s(x1)))




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(2)
BOUNDS(1, 1)