details

property	value
status	complete
benchmark	Ex4_4_Luc96b_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.0881 seconds
cpu usage	4.44495
user time	4.24486
system time	0.200086
max virtual memory	1.8543288E7
max residence set size	333036.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 10 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES (15) QDP (16) QDPOrderProof [EQUIVALENT, 0 ms] (17) QDP (18) DependencyGraphProof [EQUIVALENT, 0 ms] (19) QDP (20) UsableRulesProof [EQUIVALENT, 0 ms] (21) QDP (22) QDPSizeChangeProof [EQUIVALENT, 0 ms] (23) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(g(X), Y)) -> mark(f(X, f(g(X), Y))) mark(f(X1, X2)) -> active(f(mark(X1), X2)) mark(g(X)) -> active(g(mark(X))) f(mark(X1), X2) -> f(X1, X2) f(X1, mark(X2)) -> f(X1, X2) f(active(X1), X2) -> f(X1, X2) f(X1, active(X2)) -> f(X1, X2) g(mark(X)) -> g(X) g(active(X)) -> g(X) Q is empty. ---------------------------------------- (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(g(X), Y)) -> MARK(f(X, f(g(X), Y))) ACTIVE(f(g(X), Y)) -> F(X, f(g(X), Y)) MARK(f(X1, X2)) -> ACTIVE(f(mark(X1), X2)) MARK(f(X1, X2)) -> F(mark(X1), X2) MARK(f(X1, X2)) -> MARK(X1) MARK(g(X)) -> ACTIVE(g(mark(X))) MARK(g(X)) -> G(mark(X)) MARK(g(X)) -> MARK(X) F(mark(X1), X2) -> F(X1, X2) F(X1, mark(X2)) -> F(X1, X2) F(active(X1), X2) -> F(X1, X2) F(X1, active(X2)) -> F(X1, X2) G(mark(X)) -> G(X) G(active(X)) -> G(X) The TRS R consists of the following rules: active(f(g(X), Y)) -> mark(f(X, f(g(X), Y))) mark(f(X1, X2)) -> active(f(mark(X1), X2)) mark(g(X)) -> active(g(mark(X))) f(mark(X1), X2) -> f(X1, X2) f(X1, mark(X2)) -> f(X1, X2) f(active(X1), X2) -> f(X1, X2) f(X1, active(X2)) -> f(X1, X2) g(mark(X)) -> g(X) g(active(X)) -> g(X) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 3 less nodes. ---------------------------------------- (4) Complex Obligation (AND) popout

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all output return to TRS Standard