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TRS Stand 20472 pair #381713268
details
property
value
status
complete
benchmark
divExp.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.90776991844 seconds
cpu usage
4.60113098
max memory
3.42765568E8
stage attributes
key
value
output-size
13156
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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) QDPOrderProof [EQUIVALENT, 18 ms] (20) QDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QReductionProof [EQUIVALENT, 0 ms] (27) QDP (28) QDPQMonotonicMRRProof [EQUIVALENT, 0 ms] (29) QDP (30) DependencyGraphProof [EQUIVALENT, 0 ms] (31) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: minus(x, x) -> 0 minus(s(x), s(y)) -> minus(x, y) minus(0, x) -> 0 minus(x, 0) -> x div(s(x), s(y)) -> s(div(minus(x, y), s(y))) div(0, s(y)) -> 0 f(x, 0, b) -> x f(x, s(y), b) -> div(f(x, minus(s(y), s(0)), b), b) 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(s(x), s(y)) -> minus(x, y) minus(0, x) -> 0 minus(x, 0) -> x div(s(x), s(y)) -> s(div(minus(x, y), s(y))) div(0, s(y)) -> 0 f(x, 0, b) -> x f(x, s(y), b) -> div(f(x, minus(s(y), s(0)), b), b) The set Q consists of the following terms: minus(x0, x0) minus(s(x0), s(x1)) minus(0, x0) minus(x0, 0) div(s(x0), s(x1)) div(0, s(x0)) f(x0, 0, x1) f(x0, s(x1), x2) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT)
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