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TRS Standard pair #516966285
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
n028.star.cs.uiowa.edu
space
MNZ_10
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
30.5893931389 seconds
cpu usage
89.42203458
max memory
3.029020672E9
stage attributes
key
value
output-size
47721
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 9 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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, 169 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) AND (13) QDP (14) TransformationProof [EQUIVALENT, 0 ms] (15) QDP (16) DependencyGraphProof [EQUIVALENT, 0 ms] (17) QDP (18) TransformationProof [EQUIVALENT, 0 ms] (19) QDP (20) DependencyGraphProof [EQUIVALENT, 0 ms] (21) QDP (22) TransformationProof [EQUIVALENT, 0 ms] (23) QDP (24) DependencyGraphProof [EQUIVALENT, 0 ms] (25) QDP (26) TransformationProof [EQUIVALENT, 0 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) QDP (30) TransformationProof [EQUIVALENT, 0 ms] (31) QDP (32) DependencyGraphProof [EQUIVALENT, 0 ms] (33) QDP (34) TransformationProof [EQUIVALENT, 4 ms] (35) QDP (36) DependencyGraphProof [EQUIVALENT, 0 ms] (37) QDP (38) QDPOrderProof [EQUIVALENT, 77 ms] (39) QDP (40) QDPOrderProof [EQUIVALENT, 1351 ms] (41) QDP (42) QDPOrderProof [EQUIVALENT, 977 ms] (43) QDP (44) QDPOrderProof [EQUIVALENT, 914 ms] (45) QDP (46) QDPOrderProof [EQUIVALENT, 912 ms] (47) QDP (48) QDPOrderProof [EQUIVALENT, 689 ms] (49) QDP (50) QDPOrderProof [EQUIVALENT, 1259 ms] (51) QDP (52) DependencyGraphProof [EQUIVALENT, 0 ms] (53) TRUE (54) QDP (55) UsableRulesProof [EQUIVALENT, 0 ms] (56) QDP (57) QDPSizeChangeProof [EQUIVALENT, 0 ms] (58) 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.
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