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TRS Stand 20472 pair #381715352
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
n094.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.11918401718 seconds
cpu usage
9.10259039
max memory
5.51518208E8
stage attributes
key
value
output-size
15826
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 47 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 721 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)
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