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TRS Standard pair #516965535
details
property
value
status
complete
benchmark
z13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n005.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.260201931 seconds
cpu usage
5.874020016
max memory
4.7126528E8
stage attributes
key
value
output-size
12034
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) UsableRulesProof [EQUIVALENT, 0 ms] (6) QDP (7) QReductionProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPToSRSProof [SOUND, 0 ms] (10) QTRS (11) DependencyPairsProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QDP (16) UsableRulesProof [EQUIVALENT, 0 ms] (17) QDP (18) DependencyGraphProof [EQUIVALENT, 0 ms] (19) QDP (20) MNOCProof [EQUIVALENT, 0 ms] (21) QDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) QDP (24) QReductionProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES (28) QDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) QDP (31) DependencyGraphProof [EQUIVALENT, 0 ms] (32) QDP (33) MNOCProof [EQUIVALENT, 0 ms] (34) QDP (35) UsableRulesProof [EQUIVALENT, 0 ms] (36) QDP (37) QReductionProof [EQUIVALENT, 0 ms] (38) QDP (39) QDPSizeChangeProof [EQUIVALENT, 0 ms] (40) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, a(b(y))) -> f(a(a(x)), y) f(x, b(a(y))) -> f(b(b(x)), y) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) Q is empty. ---------------------------------------- (1) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none The TRS R 2 is f(x, a(b(y))) -> f(a(a(x)), y) f(x, b(a(y))) -> f(b(b(x)), y) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) The signature Sigma is {f_2} ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, a(b(y))) -> f(a(a(x)), y) f(x, b(a(y))) -> f(b(b(x)), y) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) The set Q consists of the following terms: f(x0, a(b(x1))) f(x0, b(a(x1))) f(a(x0), x1) f(b(x0), x1)
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