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TRS Standard pair #516965715
details
property
value
status
complete
benchmark
z07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n112.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.45002508163 seconds
cpu usage
6.516882416
max memory
4.78928896E8
stage attributes
key
value
output-size
7869
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) ATransformationProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) UsableRulesReductionPairsProof [EQUIVALENT, 10 ms] (16) QDP (17) QDPOrderProof [EQUIVALENT, 0 ms] (18) QDP (19) PisEmptyProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a, x) -> f(b, f(c, x)) f(a, f(b, x)) -> f(b, f(a, x)) f(d, f(c, x)) -> f(d, f(a, x)) f(a, f(c, x)) -> f(c, f(a, 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, x) -> F(b, f(c, x)) F(a, x) -> F(c, x) F(a, f(b, x)) -> F(b, f(a, x)) F(a, f(b, x)) -> F(a, x) F(d, f(c, x)) -> F(d, f(a, x)) F(d, f(c, x)) -> F(a, x) F(a, f(c, x)) -> F(c, f(a, x)) F(a, f(c, x)) -> F(a, x) The TRS R consists of the following rules: f(a, x) -> f(b, f(c, x)) f(a, f(b, x)) -> f(b, f(a, x)) f(d, f(c, x)) -> f(d, f(a, x)) f(a, f(c, x)) -> f(c, f(a, 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 2 SCCs with 5 less nodes. ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Q DP problem: The TRS P consists of the following rules: F(a, f(c, x)) -> F(a, x) F(a, f(b, x)) -> F(a, x) The TRS R consists of the following rules:
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