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TRS Stand 20472 pair #381711611
details
property
value
status
complete
benchmark
gcd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n096.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
13.5041091442 seconds
cpu usage
36.906503295
max memory
2.23555584E9
stage attributes
key
value
output-size
54336
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 10 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 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) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (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) QReductionProof [EQUIVALENT, 0 ms] (32) QDP (33) NonInfProof [EQUIVALENT, 46 ms] (34) QDP (35) TransformationProof [EQUIVALENT, 0 ms] (36) QDP (37) DependencyGraphProof [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) TransformationProof [EQUIVALENT, 0 ms] (50) QDP (51) Induction-Processor [SOUND, 46 ms] (52) AND (53) QDP (54) DependencyGraphProof [EQUIVALENT, 0 ms] (55) TRUE (56) QTRS (57) QTRSRRRProof [EQUIVALENT, 49 ms] (58) QTRS (59) RisEmptyProof [EQUIVALENT, 0 ms] (60) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: minus(s(x), y) -> if(gt(s(x), y), x, y) if(true, x, y) -> s(minus(x, y)) if(false, x, y) -> 0 gcd(x, y) -> if1(ge(x, y), x, y) if1(true, x, y) -> if2(gt(y, 0), x, y) if1(false, x, y) -> gcd(y, x) if2(true, x, y) -> gcd(minus(x, y), y) if2(false, x, y) -> x gt(0, y) -> false gt(s(x), 0) -> true gt(s(x), s(y)) -> gt(x, y) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) Q is empty.
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