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TRS Inner 89993 pair #381733523
details
property
value
status
complete
benchmark
innermost5.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
Mixed_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.83535718918 seconds
cpu usage
3.91814047
max memory
2.56892928E8
stage attributes
key
value
output-size
11671
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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, 1 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 1 ms] (18) YES (19) QDP (20) UsableRulesProof [EQUIVALENT, 0 ms] (21) QDP (22) QReductionProof [EQUIVALENT, 0 ms] (23) QDP (24) QDPQMonotonicMRRProof [EQUIVALENT, 27 ms] (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QDPOrderProof [EQUIVALENT, 0 ms] (29) QDP (30) PisEmptyProof [EQUIVALENT, 0 ms] (31) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(s(x), y, b) -> f(g(h(x)), y, i(y)) g(h(x)) -> g(x) g(s(x)) -> s(x) g(0) -> s(0) h(0) -> a i(0) -> b i(s(y)) -> i(y) The set Q consists of the following terms: f(s(x0), x1, b) g(h(x0)) g(s(x0)) g(0) h(0) i(0) i(s(x0)) ---------------------------------------- (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: F(s(x), y, b) -> F(g(h(x)), y, i(y)) F(s(x), y, b) -> G(h(x)) F(s(x), y, b) -> H(x) F(s(x), y, b) -> I(y) G(h(x)) -> G(x) I(s(y)) -> I(y) The TRS R consists of the following rules: f(s(x), y, b) -> f(g(h(x)), y, i(y)) g(h(x)) -> g(x) g(s(x)) -> s(x) g(0) -> s(0) h(0) -> a i(0) -> b i(s(y)) -> i(y)
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