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TRS Stand 20472 pair #381716402
details
property
value
status
complete
benchmark
PEANO_nokinds_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.64807105064 seconds
cpu usage
7.17035104
max memory
3.92781824E8
stage attributes
key
value
output-size
18065
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 36 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) QDPOrderProof [EQUIVALENT, 128 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) a__U12(tt) -> tt a__U21(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__plus(N, 0) -> a__U31(a__isNat(N), N) a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(X1, X2, X3) -> U42(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) 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: A__U11(tt, V2) -> A__U12(a__isNat(V2)) A__U11(tt, V2) -> A__ISNAT(V2) A__U31(tt, N) -> MARK(N) A__U41(tt, M, N) -> A__U42(a__isNat(N), M, N) A__U41(tt, M, N) -> A__ISNAT(N) A__U42(tt, M, N) -> A__PLUS(mark(N), mark(M)) A__U42(tt, M, N) -> MARK(N) A__U42(tt, M, N) -> MARK(M) A__ISNAT(plus(V1, V2)) -> A__U11(a__isNat(V1), V2) A__ISNAT(plus(V1, V2)) -> A__ISNAT(V1) A__ISNAT(s(V1)) -> A__U21(a__isNat(V1)) A__ISNAT(s(V1)) -> A__ISNAT(V1) A__PLUS(N, 0) -> A__U31(a__isNat(N), N) A__PLUS(N, 0) -> A__ISNAT(N) A__PLUS(N, s(M)) -> A__U41(a__isNat(M), M, N)
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