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TRS Stand 20472 pair #381710295
details
property
value
status
complete
benchmark
thiemann31.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.45836305618 seconds
cpu usage
8.989597973
max memory
4.73575424E8
stage attributes
key
value
output-size
22067
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 14 ms] (2) QTRS (3) DependencyPairsProof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) NonInfProof [EQUIVALENT, 56 ms] (20) QDP (21) DependencyGraphProof [EQUIVALENT, 0 ms] (22) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) mod(x, 0) -> modZeroErro mod(x, s(y)) -> modIter(x, s(y), 0, 0) modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) if(true, x, y, z, u) -> u if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) if2(false, x, y, z, u) -> modIter(x, y, z, u) if2(true, x, y, z, u) -> modIter(x, y, z, 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: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) mod(x, 0) -> modZeroErro mod(x, s(y)) -> modIter(x, s(y), 0, 0) modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) if(true, x, y, z, u) -> u if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) if2(false, x, y, z, u) -> modIter(x, y, z, u) if2(true, x, y, z, u) -> modIter(x, y, z, 0) The set Q consists of the following terms: le(0, x0) le(s(x0), 0) le(s(x0), s(x1)) mod(x0, 0) mod(x0, s(x1)) modIter(x0, s(x1), x2, x3) if(true, x0, x1, x2, x3) if(false, x0, x1, x2, x3) if2(false, x0, x1, x2, x3) if2(true, x0, x1, x2, x3) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ----------------------------------------
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