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SRS Stand 10685 pair #381717105
details
property
value
status
complete
benchmark
aprove2.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
Secret_05_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
9.20577907562 seconds
cpu usage
33.082075381
max memory
4.373778432E9
stage attributes
key
value
output-size
10550
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 12 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) UsableRulesProof [EQUIVALENT, 0 ms] (21) QDP (22) QDPOrderProof [EQUIVALENT, 119 ms] (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(h(x1)) -> g(f(s(x1))) f(s(s(s(x1)))) -> h(f(s(h(x1)))) f(h(x1)) -> h(f(s(h(x1)))) h(x1) -> x1 f(f(s(s(x1)))) -> s(s(s(f(f(x1))))) b(a(x1)) -> a(b(x1)) a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: h(g(x1)) -> s(f(g(x1))) s(s(s(f(x1)))) -> h(s(f(h(x1)))) h(f(x1)) -> h(s(f(h(x1)))) h(x1) -> x1 s(s(f(f(x1)))) -> f(f(s(s(s(x1))))) a(b(x1)) -> b(a(x1)) a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 3 + x_1 POL(b(x_1)) = 1 + x_1 POL(f(x_1)) = x_1 POL(g(x_1)) = x_1 POL(h(x_1)) = x_1 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1)
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