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TRS Standard pair #487070548
details
property
value
status
complete
benchmark
MYNAT_nokinds-noand_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n183.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.44973 seconds
cpu usage
10.2217
user time
9.79109
system time
0.430595
max virtual memory
1.8503516E7
max residence set size
712272.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 697 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U11(tt, V2) -> U12(isNat(activate(V2))) U12(tt) -> tt U21(tt) -> tt U31(tt, V2) -> U32(isNat(activate(V2))) U32(tt) -> tt U41(tt, N) -> activate(N) U51(tt, M, N) -> U52(isNat(activate(N)), activate(M), activate(N)) U52(tt, M, N) -> s(plus(activate(N), activate(M))) U61(tt) -> 0 U71(tt, M, N) -> U72(isNat(activate(N)), activate(M), activate(N)) U72(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNat(n__x(V1, V2)) -> U31(isNat(activate(V1)), activate(V2)) plus(N, 0) -> U41(isNat(N), N) plus(N, s(M)) -> U51(isNat(M), M, N) x(N, 0) -> U61(isNat(N)) x(N, s(M)) -> U71(isNat(M), M, N) 0 -> n__0 plus(X1, X2) -> n__plus(X1, X2) s(X) -> n__s(X) x(X1, X2) -> n__x(X1, X2) activate(n__0) -> 0 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) activate(n__s(X)) -> s(activate(X)) activate(n__x(X1, X2)) -> x(activate(X1), activate(X2)) activate(X) -> X 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: U11^1(tt, V2) -> U12^1(isNat(activate(V2))) U11^1(tt, V2) -> ISNAT(activate(V2)) U11^1(tt, V2) -> ACTIVATE(V2) U31^1(tt, V2) -> U32^1(isNat(activate(V2))) U31^1(tt, V2) -> ISNAT(activate(V2)) U31^1(tt, V2) -> ACTIVATE(V2) U41^1(tt, N) -> ACTIVATE(N) U51^1(tt, M, N) -> U52^1(isNat(activate(N)), activate(M), activate(N)) U51^1(tt, M, N) -> ISNAT(activate(N)) U51^1(tt, M, N) -> ACTIVATE(N) U51^1(tt, M, N) -> ACTIVATE(M) U52^1(tt, M, N) -> S(plus(activate(N), activate(M))) U52^1(tt, M, N) -> PLUS(activate(N), activate(M)) U52^1(tt, M, N) -> ACTIVATE(N) U52^1(tt, M, N) -> ACTIVATE(M) U61^1(tt) -> 0^1 U71^1(tt, M, N) -> U72^1(isNat(activate(N)), activate(M), activate(N)) U71^1(tt, M, N) -> ISNAT(activate(N)) U71^1(tt, M, N) -> ACTIVATE(N) U71^1(tt, M, N) -> ACTIVATE(M) U72^1(tt, M, N) -> PLUS(x(activate(N), activate(M)), activate(N)) U72^1(tt, M, N) -> X(activate(N), activate(M)) U72^1(tt, M, N) -> ACTIVATE(N) U72^1(tt, M, N) -> ACTIVATE(M) ISNAT(n__plus(V1, V2)) -> U11^1(isNat(activate(V1)), activate(V2)) ISNAT(n__plus(V1, V2)) -> ISNAT(activate(V1)) ISNAT(n__plus(V1, V2)) -> ACTIVATE(V1) ISNAT(n__plus(V1, V2)) -> ACTIVATE(V2) ISNAT(n__s(V1)) -> U21^1(isNat(activate(V1))) ISNAT(n__s(V1)) -> ISNAT(activate(V1)) ISNAT(n__s(V1)) -> ACTIVATE(V1) ISNAT(n__x(V1, V2)) -> U31^1(isNat(activate(V1)), activate(V2)) ISNAT(n__x(V1, V2)) -> ISNAT(activate(V1))
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