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TRS_Innermost 2019-03-28 22.12 pair #432270826
details
property
value
status
complete
benchmark
MYNAT_nokinds_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
7.88069 seconds
cpu usage
19.7017
user time
19.1954
system time
0.506294
max virtual memory
3.6573072E7
max residence set size
890492.0
stage attributes
key
value
starexec-result
YES
output
19.33/7.72 YES 19.53/7.75 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 19.53/7.75 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.53/7.75 19.53/7.75 19.53/7.75 Termination w.r.t. Q of the given QTRS could be proven: 19.53/7.75 19.53/7.75 (0) QTRS 19.53/7.75 (1) DependencyPairsProof [EQUIVALENT, 84 ms] 19.53/7.75 (2) QDP 19.53/7.75 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 19.53/7.75 (4) AND 19.53/7.75 (5) QDP 19.53/7.75 (6) UsableRulesProof [EQUIVALENT, 0 ms] 19.53/7.75 (7) QDP 19.53/7.75 (8) QReductionProof [EQUIVALENT, 0 ms] 19.53/7.75 (9) QDP 19.53/7.75 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 19.53/7.75 (11) YES 19.53/7.75 (12) QDP 19.53/7.75 (13) QDPOrderProof [EQUIVALENT, 1322 ms] 19.53/7.75 (14) QDP 19.53/7.75 (15) DependencyGraphProof [EQUIVALENT, 0 ms] 19.53/7.75 (16) QDP 19.53/7.75 (17) UsableRulesProof [EQUIVALENT, 0 ms] 19.53/7.75 (18) QDP 19.53/7.75 (19) QReductionProof [EQUIVALENT, 0 ms] 19.53/7.75 (20) QDP 19.53/7.75 (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] 19.53/7.75 (22) YES 19.53/7.75 19.53/7.75 19.53/7.75 ---------------------------------------- 19.53/7.75 19.53/7.75 (0) 19.53/7.75 Obligation: 19.53/7.75 Q restricted rewrite system: 19.53/7.75 The TRS R consists of the following rules: 19.53/7.75 19.53/7.75 a__U11(tt, V2) -> a__U12(a__isNat(V2)) 19.53/7.75 a__U12(tt) -> tt 19.53/7.75 a__U21(tt) -> tt 19.53/7.75 a__U31(tt, V2) -> a__U32(a__isNat(V2)) 19.53/7.75 a__U32(tt) -> tt 19.53/7.75 a__U41(tt, N) -> mark(N) 19.53/7.75 a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N) 19.53/7.75 a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) 19.53/7.75 a__U61(tt) -> 0 19.53/7.75 a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N) 19.53/7.75 a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 19.53/7.75 a__isNat(0) -> tt 19.53/7.75 a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) 19.53/7.75 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 19.53/7.75 a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2) 19.53/7.75 a__plus(N, 0) -> a__U41(a__isNat(N), N) 19.53/7.75 a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N) 19.53/7.75 a__x(N, 0) -> a__U61(a__isNat(N)) 19.53/7.75 a__x(N, s(M)) -> a__U71(a__isNat(M), M, N) 19.53/7.75 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 19.53/7.75 mark(U12(X)) -> a__U12(mark(X)) 19.53/7.75 mark(isNat(X)) -> a__isNat(X) 19.53/7.75 mark(U21(X)) -> a__U21(mark(X)) 19.53/7.75 mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 19.53/7.75 mark(U32(X)) -> a__U32(mark(X)) 19.53/7.75 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 19.53/7.75 mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) 19.53/7.75 mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) 19.53/7.75 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 19.53/7.75 mark(U61(X)) -> a__U61(mark(X)) 19.53/7.75 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 19.53/7.75 mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3) 19.53/7.75 mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 19.53/7.75 mark(tt) -> tt 19.53/7.75 mark(s(X)) -> s(mark(X)) 19.53/7.75 mark(0) -> 0 19.53/7.75 a__U11(X1, X2) -> U11(X1, X2) 19.53/7.75 a__U12(X) -> U12(X) 19.53/7.75 a__isNat(X) -> isNat(X) 19.53/7.75 a__U21(X) -> U21(X) 19.53/7.75 a__U31(X1, X2) -> U31(X1, X2) 19.53/7.75 a__U32(X) -> U32(X) 19.53/7.75 a__U41(X1, X2) -> U41(X1, X2) 19.53/7.75 a__U51(X1, X2, X3) -> U51(X1, X2, X3) 19.53/7.75 a__U52(X1, X2, X3) -> U52(X1, X2, X3) 19.53/7.75 a__plus(X1, X2) -> plus(X1, X2) 19.53/7.75 a__U61(X) -> U61(X) 19.53/7.75 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 19.53/7.75 a__U72(X1, X2, X3) -> U72(X1, X2, X3) 19.53/7.75 a__x(X1, X2) -> x(X1, X2) 19.53/7.75 19.53/7.75 The set Q consists of the following terms: 19.53/7.75 19.53/7.75 mark(U11(x0, x1)) 19.53/7.75 mark(U12(x0)) 19.53/7.75 mark(isNat(x0)) 19.53/7.75 mark(U21(x0)) 19.53/7.75 mark(U31(x0, x1)) 19.53/7.75 mark(U32(x0)) 19.53/7.75 mark(U41(x0, x1)) 19.53/7.75 mark(U51(x0, x1, x2))
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