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TRS Stand 20472 pair #381711289
details
property
value
status
complete
benchmark
thiemann34.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
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.73805379868 seconds
cpu usage
13.080149361
max memory
1.626927104E9
stage attributes
key
value
output-size
26459
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 1 ms] (2) QTRS (3) DependencyPairsProof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) TransformationProof [EQUIVALENT, 0 ms] (27) QDP (28) UsableRulesProof [EQUIVALENT, 0 ms] (29) QDP (30) QReductionProof [EQUIVALENT, 0 ms] (31) QDP (32) NonInfProof [EQUIVALENT, 61 ms] (33) AND (34) QDP (35) DependencyGraphProof [EQUIVALENT, 0 ms] (36) TRUE (37) QDP (38) DependencyGraphProof [EQUIVALENT, 0 ms] (39) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: gt(s(x), 0) -> true gt(0, y) -> false gt(s(x), s(y)) -> gt(x, y) divides(x, y) -> div(x, y, y) div(0, 0, z) -> true div(0, s(x), z) -> false div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) div(s(x), s(y), z) -> div(x, y, z) prime(x) -> test(x, s(s(0))) test(x, y) -> if1(gt(x, y), x, y) if1(true, x, y) -> if2(divides(x, y), x, y) if1(false, x, y) -> true if2(true, x, y) -> false if2(false, x, y) -> test(x, s(y)) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: gt(s(x), 0) -> true gt(0, y) -> false gt(s(x), s(y)) -> gt(x, y) divides(x, y) -> div(x, y, y) div(0, 0, z) -> true div(0, s(x), z) -> false div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) div(s(x), s(y), z) -> div(x, y, z) prime(x) -> test(x, s(s(0))) test(x, y) -> if1(gt(x, y), x, y)
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