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TRS Stand 20472 pair #381712309
details
property
value
status
complete
benchmark
otto05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n087.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.11319589615 seconds
cpu usage
5.105797896
max memory
3.37702912E8
stage attributes
key
value
output-size
13736
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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) QDPOrderProof [EQUIVALENT, 52 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) logarithm(x) -> ifa(lt(0, x), x) ifa(true, x) -> help(x, 1) ifa(false, x) -> logZeroError help(x, y) -> ifb(lt(y, x), x, y) ifb(true, x, y) -> help(half(x), s(y)) ifb(false, x, y) -> y half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) 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: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) logarithm(x) -> ifa(lt(0, x), x) ifa(true, x) -> help(x, 1) ifa(false, x) -> logZeroError help(x, y) -> ifb(lt(y, x), x, y) ifb(true, x, y) -> help(half(x), s(y)) ifb(false, x, y) -> y half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) The set Q consists of the following terms: lt(0, s(x0)) lt(x0, 0) lt(s(x0), s(x1)) logarithm(x0) ifa(true, x0) ifa(false, x0) help(x0, x1)
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