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TRS Inner 89993 pair #381733547
details
property
value
status
complete
benchmark
cade13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
Mixed_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.19394111633 seconds
cpu usage
7.076137835
max memory
3.8793216E8
stage attributes
key
value
output-size
18183
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 13 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QReductionProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) UsableRulesProof [EQUIVALENT, 0 ms] (21) QDP (22) QReductionProof [EQUIVALENT, 0 ms] (23) QDP (24) QDPQMonotonicMRRProof [EQUIVALENT, 37 ms] (25) QDP (26) NonInfProof [EQUIVALENT, 14 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: div(x, s(y)) -> d(x, s(y), 0) d(x, s(y), z) -> cond(ge(x, z), x, y, z) cond(true, x, y, z) -> s(d(x, s(y), plus(s(y), z))) cond(false, x, y, z) -> 0 ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) plus(n, 0) -> n plus(n, s(m)) -> s(plus(n, m)) plus(plus(n, m), u) -> plus(n, plus(m, u)) The set Q consists of the following terms: div(x0, s(x1)) d(x0, s(x1), x2) cond(true, x0, x1, x2) cond(false, x0, x1, x2) ge(x0, 0) ge(0, s(x0)) ge(s(x0), s(x1)) plus(x0, 0) plus(x0, s(x1)) plus(plus(x0, x1), x2) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: DIV(x, s(y)) -> D(x, s(y), 0) D(x, s(y), z) -> COND(ge(x, z), x, y, z) D(x, s(y), z) -> GE(x, z) COND(true, x, y, z) -> D(x, s(y), plus(s(y), z)) COND(true, x, y, z) -> PLUS(s(y), z) GE(s(u), s(v)) -> GE(u, v) PLUS(n, s(m)) -> PLUS(n, m) PLUS(plus(n, m), u) -> PLUS(n, plus(m, u)) PLUS(plus(n, m), u) -> PLUS(m, u) The TRS R consists of the following rules:
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