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TRS Stand 20472 pair #381715387
details
property
value
status
complete
benchmark
Ex4_7_56_Bor03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.7048740387 seconds
cpu usage
15.128587179
max memory
1.129054208E9
stage attributes
key
value
output-size
25715
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 18 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 103 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 32 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 43 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 49 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 66 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QDP (16) QDPOrderProof [EQUIVALENT, 12 ms] (17) QDP (18) PisEmptyProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPOrderProof [EQUIVALENT, 7 ms] (22) QDP (23) QDPOrderProof [EQUIVALENT, 23 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) QDP (27) UsableRulesProof [EQUIVALENT, 0 ms] (28) QDP (29) QDPSizeChangeProof [EQUIVALENT, 0 ms] (30) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__from(X) -> cons(mark(X), from(s(X))) a__after(0, XS) -> mark(XS) a__after(s(N), cons(X, XS)) -> a__after(mark(N), mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1, X2)) -> a__after(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__from(X) -> from(X) a__after(X1, X2) -> after(X1, X2) 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: A__FROM(X) -> MARK(X) A__AFTER(0, XS) -> MARK(XS) A__AFTER(s(N), cons(X, XS)) -> A__AFTER(mark(N), mark(XS)) A__AFTER(s(N), cons(X, XS)) -> MARK(N) A__AFTER(s(N), cons(X, XS)) -> MARK(XS) MARK(from(X)) -> A__FROM(mark(X)) MARK(from(X)) -> MARK(X) MARK(after(X1, X2)) -> A__AFTER(mark(X1), mark(X2)) MARK(after(X1, X2)) -> MARK(X1) MARK(after(X1, X2)) -> MARK(X2) MARK(cons(X1, X2)) -> MARK(X1) MARK(s(X)) -> MARK(X) The TRS R consists of the following rules: a__from(X) -> cons(mark(X), from(s(X))) a__after(0, XS) -> mark(XS) a__after(s(N), cons(X, XS)) -> a__after(mark(N), mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1, X2)) -> a__after(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0
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