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TRS Inner 89993 pair #381733989
details
property
value
status
complete
benchmark
Ex14_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n112.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.80220580101 seconds
cpu usage
3.98291678
max memory
2.5552896E8
stage attributes
key
value
output-size
14294
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 32 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) MRRProof [EQUIVALENT, 0 ms] (6) QDP (7) TransformationProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) TransformationProof [EQUIVALENT, 0 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) QReductionProof [EQUIVALENT, 0 ms] (24) QDP (25) TransformationProof [EQUIVALENT, 0 ms] (26) QDP (27) DependencyGraphProof [EQUIVALENT, 0 ms] (28) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__h(X) -> a__g(mark(X), X) a__g(a, X) -> a__f(b, X) a__f(X, X) -> a__h(a__a) a__a -> b mark(h(X)) -> a__h(mark(X)) mark(g(X1, X2)) -> a__g(mark(X1), X2) mark(a) -> a__a mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(b) -> b a__h(X) -> h(X) a__g(X1, X2) -> g(X1, X2) a__a -> a a__f(X1, X2) -> f(X1, X2) The set Q consists of the following terms: a__h(x0) a__a mark(h(x0)) mark(g(x0, x1)) mark(a) mark(f(x0, x1)) mark(b) a__g(x0, x1) a__f(x0, x1) ---------------------------------------- (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: A__H(X) -> A__G(mark(X), X) A__H(X) -> MARK(X) A__G(a, X) -> A__F(b, X) A__F(X, X) -> A__H(a__a) A__F(X, X) -> A__A MARK(h(X)) -> A__H(mark(X)) MARK(h(X)) -> MARK(X) MARK(g(X1, X2)) -> A__G(mark(X1), X2) MARK(g(X1, X2)) -> MARK(X1) MARK(a) -> A__A MARK(f(X1, X2)) -> A__F(mark(X1), X2)
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