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TRS Inner 89993 pair #381733660
details
property
value
status
complete
benchmark
#4.37a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n010.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.40458989143 seconds
cpu usage
3.684299006
max memory
2.48651776E8
stage attributes
key
value
output-size
7481
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 59 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 1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) MRRProof [EQUIVALENT, 0 ms] (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) MRRProof [EQUIVALENT, 0 ms] (22) QDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(c(s(x), y)) -> f(c(x, s(y))) g(c(x, s(y))) -> g(c(s(x), y)) g(s(f(x))) -> g(f(x)) The set Q consists of the following terms: f(c(s(x0), x1)) g(c(x0, s(x1))) g(s(f(x0))) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(c(x_1, x_2)) = 2*x_1 + 2*x_2 POL(f(x_1)) = 2*x_1 POL(g(x_1)) = 2*x_1 POL(s(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(s(f(x))) -> g(f(x)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(c(s(x), y)) -> f(c(x, s(y))) g(c(x, s(y))) -> g(c(s(x), y)) The set Q consists of the following terms: f(c(s(x0), x1)) g(c(x0, s(x1))) g(s(f(x0))) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation:
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