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TRS Stand 20472 pair #381711130
details
property
value
status
complete
benchmark
quot.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.43191504478 seconds
cpu usage
9.25937863
max memory
3.64724224E8
stage attributes
key
value
output-size
23891
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 14 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) QDPQMonotonicMRRProof [EQUIVALENT, 28 ms] (27) QDP (28) TransformationProof [EQUIVALENT, 1 ms] (29) QDP (30) DependencyGraphProof [EQUIVALENT, 0 ms] (31) QDP (32) UsableRulesProof [EQUIVALENT, 0 ms] (33) QDP (34) TransformationProof [EQUIVALENT, 0 ms] (35) QDP (36) DependencyGraphProof [EQUIVALENT, 0 ms] (37) QDP (38) UsableRulesProof [EQUIVALENT, 0 ms] (39) QDP (40) TransformationProof [SOUND, 0 ms] (41) QDP (42) UsableRulesProof [EQUIVALENT, 0 ms] (43) QDP (44) QReductionProof [EQUIVALENT, 0 ms] (45) QDP (46) TransformationProof [EQUIVALENT, 0 ms] (47) QDP (48) DependencyGraphProof [EQUIVALENT, 0 ms] (49) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: minus(x, x) -> 0 minus(0, x) -> 0 minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) quot(x, y) -> if_quot(minus(x, y), y, le(y, 0), le(y, x)) if_quot(x, y, true, z) -> divByZeroError if_quot(x, y, false, true) -> s(quot(x, y)) if_quot(x, y, false, false) -> 0 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(x, x) -> 0 minus(0, x) -> 0 minus(x, 0) -> x
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