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TRS Stand 20472 pair #381710125
details
property
value
status
complete
benchmark
thiemann01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n110.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.91830897331 seconds
cpu usage
4.571688561
max memory
2.77393408E8
stage attributes
key
value
output-size
18020
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 1 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) DependencyGraphProof [EQUIVALENT, 0 ms] (29) QDP (30) UsableRulesProof [EQUIVALENT, 0 ms] (31) QDP (32) QReductionProof [EQUIVALENT, 0 ms] (33) QDP (34) QDPQMonotonicMRRProof [EQUIVALENT, 32 ms] (35) QDP (36) DependencyGraphProof [EQUIVALENT, 0 ms] (37) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: minus(0, y) -> 0 minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) plus(0, y) -> y plus(s(x), y) -> plus(x, s(y)) zero(s(x)) -> false zero(0) -> true p(s(x)) -> x div(x, y) -> quot(x, y, 0) quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0))) if(true, x, y, z) -> p(z) if(false, x, s(y), z) -> quot(minus(x, s(y)), s(y), z) 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: minus(0, y) -> 0 minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) plus(0, y) -> y plus(s(x), y) -> plus(x, s(y)) zero(s(x)) -> false zero(0) -> true p(s(x)) -> x div(x, y) -> quot(x, y, 0) quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0))) if(true, x, y, z) -> p(z) if(false, x, s(y), z) -> quot(minus(x, s(y)), s(y), z) The set Q consists of the following terms:
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