/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(?, O(1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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


The TRS R consists of the following rules:

   p(f(f(x))) -> q(f(g(x)))
   p(g(g(x))) -> q(g(f(x)))
   q(f(f(x))) -> p(f(g(x)))
   q(g(g(x))) -> p(g(f(x)))

S is empty.
Rewrite Strategy: FULL
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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:

q(g(g(x0))) ->^* p(g(f(x0)))

q(f(f(x0))) ->^* p(f(g(x0)))

p(g(g(x0))) ->^* q(g(f(x0)))

p(f(f(x0))) ->^* q(f(g(x0)))




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(2)
BOUNDS(1, 1)