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TRS Inner 89993 pair #381733893
details
property
value
status
complete
benchmark
Ex9_Luc06_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.91344594955 seconds
cpu usage
4.372645053
max memory
2.58260992E8
stage attributes
key
value
output-size
21399
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 12 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QReductionProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) MRRProof [EQUIVALENT, 27 ms] (14) QDP (15) TransformationProof [EQUIVALENT, 0 ms] (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) TransformationProof [EQUIVALENT, 0 ms] (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) UsableRulesProof [EQUIVALENT, 0 ms] (26) QDP (27) TransformationProof [EQUIVALENT, 0 ms] (28) QDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) QDP (31) TransformationProof [EQUIVALENT, 0 ms] (32) QDP (33) DependencyGraphProof [EQUIVALENT, 0 ms] (34) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(a, X, X)) -> mark(f(X, b, b)) active(b) -> mark(a) mark(f(X1, X2, X3)) -> active(f(X1, mark(X2), X3)) mark(a) -> active(a) mark(b) -> active(b) f(mark(X1), X2, X3) -> f(X1, X2, X3) f(X1, mark(X2), X3) -> f(X1, X2, X3) f(X1, X2, mark(X3)) -> f(X1, X2, X3) f(active(X1), X2, X3) -> f(X1, X2, X3) f(X1, active(X2), X3) -> f(X1, X2, X3) f(X1, X2, active(X3)) -> f(X1, X2, X3) The set Q consists of the following terms: active(f(a, x0, x0)) active(b) mark(f(x0, x1, x2)) mark(a) mark(b) f(mark(x0), x1, x2) f(x0, mark(x1), x2) f(x0, x1, mark(x2)) f(active(x0), x1, x2) f(x0, active(x1), x2) f(x0, x1, active(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: ACTIVE(f(a, X, X)) -> MARK(f(X, b, b)) ACTIVE(f(a, X, X)) -> F(X, b, b) ACTIVE(b) -> MARK(a) MARK(f(X1, X2, X3)) -> ACTIVE(f(X1, mark(X2), X3)) MARK(f(X1, X2, X3)) -> F(X1, mark(X2), X3)
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