details

property	value
status	complete
benchmark	z08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n168.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.26407599449 seconds
cpu usage	5.911231084
max memory	4.72387584E8

stage attributes

key	value
output-size	4444
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) UsableRulesReductionPairsProof [EQUIVALENT, 18 ms] (6) QDP (7) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a, f(b, f(a, x))) -> f(a, f(b, f(b, f(a, x)))) f(b, f(b, f(b, x))) -> f(b, f(b, x)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: F(a, f(b, f(a, x))) -> F(a, f(b, f(b, f(a, x)))) F(a, f(b, f(a, x))) -> F(b, f(b, f(a, x))) The TRS R consists of the following rules: f(a, f(b, f(a, x))) -> f(a, f(b, f(b, f(a, x)))) f(b, f(b, f(b, x))) -> f(b, f(b, x)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(a, f(b, f(a, x))) -> F(a, f(b, f(b, f(a, x)))) The TRS R consists of the following rules: f(a, f(b, f(a, x))) -> f(a, f(b, f(b, f(a, x)))) f(b, f(b, f(b, x))) -> f(b, f(b, x)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) UsableRulesReductionPairsProof (EQUIVALENT) First, we A-transformed [FROCOS05] the QDP-Problem. Then we obtain the following A-transformed DP problem. The pairs P are: a1(b(a(x))) -> a1(b(b(a(x)))) and the Q and R are: Q restricted rewrite system: The TRS R consists of the following rules: a(b(a(x))) -> a(b(b(a(x)))) b(b(b(x))) -> b(b(x)) Q is empty. By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well. No dependency pairs are removed. popout

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