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TRS Stand 20472 pair #381711935
details
property
value
status
complete
benchmark
z06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n047.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.71788907051 seconds
cpu usage
3.720757418
max memory
1.94588672E8
stage attributes
key
value
output-size
10411
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) DependencyGraphProof [EQUIVALENT, 0 ms] (9) QDP (10) MNOCProof [EQUIVALENT, 0 ms] (11) QDP (12) UsableRulesProof [EQUIVALENT, 0 ms] (13) QDP (14) ATransformationProof [EQUIVALENT, 0 ms] (15) QDP (16) QReductionProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) QDP (25) MNOCProof [EQUIVALENT, 0 ms] (26) QDP (27) UsableRulesProof [EQUIVALENT, 0 ms] (28) QDP (29) ATransformationProof [EQUIVALENT, 0 ms] (30) QDP (31) QReductionProof [EQUIVALENT, 0 ms] (32) QDP (33) QDPSizeChangeProof [EQUIVALENT, 0 ms] (34) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a, f(b, x)) -> f(a, f(a, f(a, x))) f(b, f(a, x)) -> f(b, 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, x)) -> F(a, f(a, f(a, x))) F(a, f(b, x)) -> F(a, f(a, x)) F(a, f(b, x)) -> F(a, x) F(b, f(a, x)) -> F(b, f(b, f(b, x))) F(b, f(a, x)) -> F(b, f(b, x)) F(b, f(a, x)) -> F(b, x) The TRS R consists of the following rules: f(a, f(b, x)) -> f(a, f(a, f(a, x))) f(b, f(a, x)) -> f(b, 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 2 SCCs. ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation:
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