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TRS Innermost pair #487093375
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
n149.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.47729 seconds
cpu usage
14.434
user time
13.7834
system time
0.650567
max virtual memory
3.7116104E7
max residence set size
1091236.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 24 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 56 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 25 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 62 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 11 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 15 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QDP (16) QDPQMonotonicMRRProof [EQUIVALENT, 11 ms] (17) QDP (18) PisEmptyProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPOrderProof [EQUIVALENT, 44 ms] (22) QDP (23) QDPOrderProof [EQUIVALENT, 8 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) QDP (27) UsableRulesProof [EQUIVALENT, 0 ms] (28) QDP (29) QReductionProof [EQUIVALENT, 0 ms] (30) QDP (31) QDPSizeChangeProof [EQUIVALENT, 0 ms] (32) 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) The set Q consists of the following terms: a__from(x0) mark(from(x0)) mark(after(x0, x1)) mark(cons(x0, x1)) mark(s(x0)) mark(0) a__after(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: 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))
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