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TRS Standard pair #487073053
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
n174.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.00805 seconds
cpu usage
13.274
user time
12.4699
system time
0.804151
max virtual memory
2.0154532E7
max residence set size
1704268.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 20 ms] (2) QTRS (3) DependencyPairsProof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, 64 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) 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)) The set Q consists of the following terms:
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