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TRS_Innermost 2019-03-28 22.12 pair #432270806
details
property
value
status
complete
benchmark
MYNAT_complete_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n153.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.12362 seconds
cpu usage
8.90153
user time
8.54647
system time
0.35506
max virtual memory
1.8454068E7
max residence set size
509148.0
stage attributes
key
value
starexec-result
YES
output
8.64/3.06 YES 8.64/3.07 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 8.64/3.07 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.64/3.07 8.64/3.07 8.64/3.07 Termination w.r.t. Q of the given QTRS could be proven: 8.64/3.07 8.64/3.07 (0) QTRS 8.64/3.07 (1) QTRSRRRProof [EQUIVALENT, 840 ms] 8.64/3.07 (2) QTRS 8.64/3.07 (3) QTRSRRRProof [EQUIVALENT, 134 ms] 8.64/3.07 (4) QTRS 8.64/3.07 (5) QTRSRRRProof [EQUIVALENT, 5 ms] 8.64/3.07 (6) QTRS 8.64/3.07 (7) RisEmptyProof [EQUIVALENT, 0 ms] 8.64/3.07 (8) YES 8.64/3.07 8.64/3.07 8.64/3.07 ---------------------------------------- 8.64/3.07 8.64/3.07 (0) 8.64/3.07 Obligation: 8.64/3.07 Q restricted rewrite system: 8.64/3.07 The TRS R consists of the following rules: 8.64/3.07 8.64/3.07 active(U11(tt, V1, V2)) -> mark(U12(isNat(V1), V2)) 8.64/3.07 active(U12(tt, V2)) -> mark(U13(isNat(V2))) 8.64/3.07 active(U13(tt)) -> mark(tt) 8.64/3.07 active(U21(tt, V1)) -> mark(U22(isNat(V1))) 8.64/3.07 active(U22(tt)) -> mark(tt) 8.64/3.07 active(U31(tt, V1, V2)) -> mark(U32(isNat(V1), V2)) 8.64/3.07 active(U32(tt, V2)) -> mark(U33(isNat(V2))) 8.64/3.07 active(U33(tt)) -> mark(tt) 8.64/3.07 active(U41(tt, N)) -> mark(N) 8.64/3.07 active(U51(tt, M, N)) -> mark(s(plus(N, M))) 8.64/3.07 active(U61(tt)) -> mark(0) 8.64/3.07 active(U71(tt, M, N)) -> mark(plus(x(N, M), N)) 8.64/3.07 active(and(tt, X)) -> mark(X) 8.64/3.07 active(isNat(0)) -> mark(tt) 8.64/3.07 active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)) 8.64/3.07 active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) 8.64/3.07 active(isNat(x(V1, V2))) -> mark(U31(and(isNatKind(V1), isNatKind(V2)), V1, V2)) 8.64/3.07 active(isNatKind(0)) -> mark(tt) 8.64/3.07 active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))) 8.64/3.07 active(isNatKind(s(V1))) -> mark(isNatKind(V1)) 8.64/3.07 active(isNatKind(x(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))) 8.64/3.07 active(plus(N, 0)) -> mark(U41(and(isNat(N), isNatKind(N)), N)) 8.64/3.07 active(plus(N, s(M))) -> mark(U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)) 8.64/3.07 active(x(N, 0)) -> mark(U61(and(isNat(N), isNatKind(N)))) 8.64/3.07 active(x(N, s(M))) -> mark(U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)) 8.64/3.07 mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) 8.64/3.07 mark(tt) -> active(tt) 8.64/3.07 mark(U12(X1, X2)) -> active(U12(mark(X1), X2)) 8.64/3.07 mark(isNat(X)) -> active(isNat(X)) 8.64/3.07 mark(U13(X)) -> active(U13(mark(X))) 8.64/3.07 mark(U21(X1, X2)) -> active(U21(mark(X1), X2)) 8.64/3.07 mark(U22(X)) -> active(U22(mark(X))) 8.64/3.07 mark(U31(X1, X2, X3)) -> active(U31(mark(X1), X2, X3)) 8.64/3.07 mark(U32(X1, X2)) -> active(U32(mark(X1), X2)) 8.64/3.07 mark(U33(X)) -> active(U33(mark(X))) 8.64/3.07 mark(U41(X1, X2)) -> active(U41(mark(X1), X2)) 8.64/3.07 mark(U51(X1, X2, X3)) -> active(U51(mark(X1), X2, X3)) 8.64/3.07 mark(s(X)) -> active(s(mark(X))) 8.64/3.07 mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 8.64/3.07 mark(U61(X)) -> active(U61(mark(X))) 8.64/3.07 mark(0) -> active(0) 8.64/3.07 mark(U71(X1, X2, X3)) -> active(U71(mark(X1), X2, X3)) 8.64/3.07 mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) 8.64/3.07 mark(and(X1, X2)) -> active(and(mark(X1), X2)) 8.64/3.07 mark(isNatKind(X)) -> active(isNatKind(X)) 8.64/3.07 U11(mark(X1), X2, X3) -> U11(X1, X2, X3) 8.64/3.07 U11(X1, mark(X2), X3) -> U11(X1, X2, X3) 8.64/3.07 U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) 8.64/3.07 U11(active(X1), X2, X3) -> U11(X1, X2, X3) 8.64/3.07 U11(X1, active(X2), X3) -> U11(X1, X2, X3) 8.64/3.07 U11(X1, X2, active(X3)) -> U11(X1, X2, X3) 8.64/3.07 U12(mark(X1), X2) -> U12(X1, X2) 8.64/3.07 U12(X1, mark(X2)) -> U12(X1, X2) 8.64/3.07 U12(active(X1), X2) -> U12(X1, X2) 8.64/3.07 U12(X1, active(X2)) -> U12(X1, X2) 8.64/3.07 isNat(mark(X)) -> isNat(X) 8.64/3.07 isNat(active(X)) -> isNat(X) 8.64/3.07 U13(mark(X)) -> U13(X) 8.64/3.07 U13(active(X)) -> U13(X) 8.64/3.07 U21(mark(X1), X2) -> U21(X1, X2) 8.64/3.07 U21(X1, mark(X2)) -> U21(X1, X2) 8.64/3.07 U21(active(X1), X2) -> U21(X1, X2) 8.64/3.07 U21(X1, active(X2)) -> U21(X1, X2) 8.64/3.07 U22(mark(X)) -> U22(X) 8.64/3.07 U22(active(X)) -> U22(X) 8.64/3.07 U31(mark(X1), X2, X3) -> U31(X1, X2, X3) 8.64/3.07 U31(X1, mark(X2), X3) -> U31(X1, X2, X3) 8.64/3.07 U31(X1, X2, mark(X3)) -> U31(X1, X2, X3) 8.64/3.07 U31(active(X1), X2, X3) -> U31(X1, X2, X3) 8.64/3.07 U31(X1, active(X2), X3) -> U31(X1, X2, X3) 8.64/3.07 U31(X1, X2, active(X3)) -> U31(X1, X2, X3) 8.64/3.07 U32(mark(X1), X2) -> U32(X1, X2) 8.64/3.07 U32(X1, mark(X2)) -> U32(X1, X2) 8.64/3.07 U32(active(X1), X2) -> U32(X1, X2) 8.64/3.07 U32(X1, active(X2)) -> U32(X1, X2)
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