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	n098.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	7.43671298027 seconds
cpu usage	10.12223299
max memory	6.28731904E8

stage attributes

key	value
output-size	18057
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 44 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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, 95 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) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard