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TRS Standard pair #487073843
details
property
value
status
complete
benchmark
0.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
MNZ_10
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
24.5554 seconds
cpu usage
81.8943
user time
79.6365
system time
2.25781
max virtual memory
3.7657036E7
max residence set size
3999176.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) QDP (5) TransformationProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 166 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) AND (13) QDP (14) QDPOrderProof [EQUIVALENT, 43 ms] (15) QDP (16) TransformationProof [EQUIVALENT, 0 ms] (17) QDP (18) DependencyGraphProof [EQUIVALENT, 0 ms] (19) QDP (20) TransformationProof [EQUIVALENT, 0 ms] (21) QDP (22) DependencyGraphProof [EQUIVALENT, 0 ms] (23) QDP (24) TransformationProof [EQUIVALENT, 0 ms] (25) QDP (26) DependencyGraphProof [EQUIVALENT, 0 ms] (27) QDP (28) TransformationProof [EQUIVALENT, 0 ms] (29) QDP (30) DependencyGraphProof [EQUIVALENT, 0 ms] (31) QDP (32) TransformationProof [EQUIVALENT, 29 ms] (33) QDP (34) DependencyGraphProof [EQUIVALENT, 0 ms] (35) QDP (36) TransformationProof [EQUIVALENT, 0 ms] (37) QDP (38) DependencyGraphProof [EQUIVALENT, 0 ms] (39) QDP (40) QDPOrderProof [EQUIVALENT, 37 ms] (41) QDP (42) QDPOrderProof [EQUIVALENT, 1323 ms] (43) QDP (44) QDPOrderProof [EQUIVALENT, 956 ms] (45) QDP (46) QDPOrderProof [EQUIVALENT, 811 ms] (47) QDP (48) QDPOrderProof [EQUIVALENT, 975 ms] (49) QDP (50) QDPOrderProof [EQUIVALENT, 719 ms] (51) QDP (52) QDPOrderProof [EQUIVALENT, 1166 ms] (53) QDP (54) DependencyGraphProof [EQUIVALENT, 0 ms] (55) TRUE (56) QDP (57) UsableRulesProof [EQUIVALENT, 0 ms] (58) QDP (59) QDPSizeChangeProof [EQUIVALENT, 0 ms] (60) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: s(s(0)) -> f(0) f(0) -> 0 s(s(s(0))) -> f(s(0)) f(s(0)) -> s(0) s(s(s(s(s(s(s(s(0)))))))) -> f(s(s(0))) f(s(s(0))) -> s(s(s(s(s(s(0)))))) g(x) -> h(x, x) s(x) -> h(x, 0) s(x) -> h(0, x) f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) h(f(x), g(x)) -> f(s(x)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation:
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