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TRS Inner 89993 pair #381733789
details
property
value
status
complete
benchmark
Ex1_GM99_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n004.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.32346606255 seconds
cpu usage
4.229140596
max memory
2.4786944E8
stage attributes
key
value
output-size
4563
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) QDPOrderProof [EQUIVALENT, 20 ms] (6) QDP (7) PisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(a, b, X) -> a__f(X, X, mark(X)) a__c -> a a__c -> b mark(f(X1, X2, X3)) -> a__f(X1, X2, mark(X3)) mark(c) -> a__c mark(a) -> a mark(b) -> b a__f(X1, X2, X3) -> f(X1, X2, X3) a__c -> c The set Q consists of the following terms: a__c mark(f(x0, x1, x2)) mark(c) mark(a) mark(b) a__f(x0, x1, x2) ---------------------------------------- (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__F(a, b, X) -> A__F(X, X, mark(X)) A__F(a, b, X) -> MARK(X) MARK(f(X1, X2, X3)) -> A__F(X1, X2, mark(X3)) MARK(f(X1, X2, X3)) -> MARK(X3) MARK(c) -> A__C The TRS R consists of the following rules: a__f(a, b, X) -> a__f(X, X, mark(X)) a__c -> a a__c -> b mark(f(X1, X2, X3)) -> a__f(X1, X2, mark(X3)) mark(c) -> a__c mark(a) -> a mark(b) -> b a__f(X1, X2, X3) -> f(X1, X2, X3) a__c -> c The set Q consists of the following terms: a__c mark(f(x0, x1, x2)) mark(c) mark(a) mark(b) a__f(x0, x1, x2) 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 2 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules:
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