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TRS Standard pair #487072293
details
property
value
status
complete
benchmark
5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n191.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
19.9946 seconds
cpu usage
52.015
user time
50.5244
system time
1.49052
max virtual memory
3.8062224E7
max residence set size
3907044.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) TransformationProof [EQUIVALENT, 0 ms] (9) QDP (10) DependencyGraphProof [EQUIVALENT, 0 ms] (11) TRUE (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) TransformationProof [EQUIVALENT, 0 ms] (16) QDP (17) DependencyGraphProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPOrderProof [EQUIVALENT, 500 ms] (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QDPOrderProof [EQUIVALENT, 11 ms] (29) QDP (30) PisEmptyProof [EQUIVALENT, 0 ms] (31) YES (32) QDP (33) UsableRulesProof [EQUIVALENT, 0 ms] (34) QDP (35) TransformationProof [EQUIVALENT, 0 ms] (36) QDP (37) TransformationProof [EQUIVALENT, 0 ms] (38) QDP (39) TransformationProof [EQUIVALENT, 0 ms] (40) QDP (41) DependencyGraphProof [EQUIVALENT, 0 ms] (42) QDP (43) TransformationProof [EQUIVALENT, 0 ms] (44) QDP (45) TransformationProof [EQUIVALENT, 0 ms] (46) QDP (47) TransformationProof [EQUIVALENT, 0 ms] (48) QDP (49) DependencyGraphProof [EQUIVALENT, 0 ms] (50) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(x, x, x) -> g(c, d, e) g(x, y, x) -> g(c, d, e) s(f(x, y)) -> f(y, f(s(s(x)), a)) h(h(x, a), y) -> h(h(a, y), h(a, x)) f(x, f(y, f(x, y))) -> f(a, f(x, f(y, b))) f(h(a, y), g(x, b, a)) -> h(f(x, s(y)), s(b)) h(f(x, s(y)), b) -> f(a, g(y, a, f(s(x), a))) f(x, g(x, a, f(s(x), y))) -> f(h(x, b), g(a, b, y)) s(y) -> b 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: G(x, x, x) -> G(c, d, e) G(x, y, x) -> G(c, d, e) S(f(x, y)) -> F(y, f(s(s(x)), a)) S(f(x, y)) -> F(s(s(x)), a) S(f(x, y)) -> S(s(x)) S(f(x, y)) -> S(x) H(h(x, a), y) -> H(h(a, y), h(a, x)) H(h(x, a), y) -> H(a, y) H(h(x, a), y) -> H(a, x) F(x, f(y, f(x, y))) -> F(a, f(x, f(y, b)))
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