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TRS Inner 89993 pair #381733539
details
property
value
status
complete
benchmark
test75.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
Mixed_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.08424091339 seconds
cpu usage
4.324221892
max memory
2.57466368E8
stage attributes
key
value
output-size
9557
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) QDP (5) UsableRulesProof [EQUIVALENT, 0 ms] (6) QDP (7) QReductionProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) Induction-Processor [SOUND, 6 ms] (12) AND (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) QTRS (17) QTRSRRRProof [EQUIVALENT, 0 ms] (18) QTRS (19) RisEmptyProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(0, 1, X) -> f(g(X, X), X, X) g(X, Y) -> X g(X, Y) -> Y The set Q consists of the following terms: f(0, 1, x0) g(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: F(0, 1, X) -> F(g(X, X), X, X) F(0, 1, X) -> G(X, X) The TRS R consists of the following rules: f(0, 1, X) -> f(g(X, X), X, X) g(X, Y) -> X g(X, Y) -> Y The set Q consists of the following terms: f(0, 1, x0) g(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(0, 1, X) -> F(g(X, X), X, X) The TRS R consists of the following rules: f(0, 1, X) -> f(g(X, X), X, X) g(X, Y) -> X g(X, Y) -> Y The set Q consists of the following terms:
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