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TRS Standard pair #516967505
details
property
value
status
complete
benchmark
aprove04.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n089.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
4.87448906898 seconds
cpu usage
14.962382352
max memory
8.40421376E8
stage attributes
key
value
output-size
47485
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 32 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms]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) TransformationProof [EQUIVALENT, 4 ms] (34) QDP (35) DependencyGraphProof [EQUIVALENT, 0 ms] (36) QDP (37) UsableRulesProof [EQUIVALENT, 0 ms] (38) QDP (39) QReductionProof [EQUIVALENT, 0 ms] (40) QDP (41) TransformationProof [EQUIVALENT, 0 ms] (42) QDP (43) UsableRulesProof [EQUIVALENT, 0 ms] (44) QDP (45) TransformationProof [EQUIVALENT, 0 ms] (46) QDP (47) UsableRulesProof [EQUIVALENT, 0 ms] (48) QDP (49) QReductionProof [EQUIVALENT, 0 ms] (50) QDP (51) TransformationProof [EQUIVALENT, 0 ms] (52) QDP (53) TransformationProof [EQUIVALENT, 0 ms] (54) QDP (55) QDPSizeChangeProof [EQUIVALENT, 0 ms] (56) YES (57) QDP (58) UsableRulesProof [EQUIVALENT, 0 ms] (59) QDP (60) QReductionProof [EQUIVALENT, 0 ms] (61) QDP (62) NonInfProof [EQUIVALENT, 84 ms] (63) QDP (64) DependencyGraphProof [EQUIVALENT, 0 ms] (65) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: lcm(x, y) -> lcmIter(x, y, 0, times(x, y)) lcmIter(x, y, z, u) -> if(or(ge(0, x), ge(z, u)), x, y, z, u) if(true, x, y, z, u) -> z if(false, x, y, z, u) -> if2(divisible(z, y), x, y, z, u) if2(true, x, y, z, u) -> z if2(false, x, y, z, u) -> lcmIter(x, y, plus(x, z), u) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> ifTimes(ge(0, x), x, y) ifTimes(true, x, y) -> 0 ifTimes(false, x, y) -> plus(y, times(y, p(x))) p(s(x)) -> x
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