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TRS Stand 20472 pair #381709976
details
property
value
status
complete
benchmark
tpa2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n085.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.00176095963 seconds
cpu usage
4.840071467
max memory
3.18001152E8
stage attributes
key
value
output-size
9831
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 2 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPOrderProof [EQUIVALENT, 34 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 0 ms] (22) QDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: -(x, 0) -> x -(s(x), s(y)) -> -(x, y) p(s(x)) -> x f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x)))) f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x))) Q is empty. ---------------------------------------- (1) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is -(x, 0) -> x -(s(x), s(y)) -> -(x, y) p(s(x)) -> x The TRS R 2 is f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x)))) f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x))) The signature Sigma is {f_2} ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: -(x, 0) -> x -(s(x), s(y)) -> -(x, y) p(s(x)) -> x f(s(x), y) -> f(p(-(s(x), y)), p(-(y, s(x)))) f(x, s(y)) -> f(p(-(x, s(y))), p(-(s(y), x))) The set Q consists of the following terms: -(x0, 0) -(s(x0), s(x1)) p(s(x0)) f(s(x0), x1) f(x0, s(x1)) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules:
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