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TRS Innermost pair #487093429
details
property
value
status
complete
benchmark
PEANO_complete_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.08703 seconds
cpu usage
5.19798
user time
4.99026
system time
0.207718
max virtual memory
1.8408912E7
max residence set size
305084.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 316 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 24 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) a__U12(tt, V2) -> a__U13(a__isNat(V2)) a__U13(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0) -> tt a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U13(X)) -> a__U13(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2) -> U12(X1, X2) a__isNat(X) -> isNat(X) a__U13(X) -> U13(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatKind(X) -> isNatKind(X) The set Q consists of the following terms: mark(U11(x0, x1, x2)) mark(U12(x0, x1)) mark(isNat(x0)) mark(U13(x0)) mark(U21(x0, x1)) mark(U22(x0)) mark(U31(x0, x1)) mark(U41(x0, x1, x2)) mark(plus(x0, x1)) mark(and(x0, x1)) mark(isNatKind(x0)) mark(tt) mark(s(x0)) mark(0) a__U11(x0, x1, x2) a__U12(x0, x1) a__isNat(x0) a__U13(x0) a__U21(x0, x1) a__U22(x0) a__U31(x0, x1) a__U41(x0, x1, x2) a__plus(x0, x1) a__and(x0, x1) a__isNatKind(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: a__U11/3(YES,YES,YES) tt/0)
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