details

property	value
status	complete
benchmark	MYNAT_complete.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.64551 seconds
cpu usage	11.913
user time	11.2939
system time	0.619087
max virtual memory	1.858376E7
max residence set size	1334608.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSDependencyPairsProof [EQUIVALENT, 18 ms] (2) QCSDP (3) QCSDependencyGraphProof [EQUIVALENT, 5 ms] (4) AND (5) QCSDP (6) QCSDPReductionPairProof [EQUIVALENT, 97 ms] (7) QCSDP (8) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (9) AND (10) QCSDP (11) QCSDPReductionPairProof [EQUIVALENT, 207 ms] (12) QCSDP (13) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE (15) QCSDP (16) QCSDPReductionPairProof [EQUIVALENT, 307 ms] (17) QCSDP (18) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (19) TRUE (20) QCSDP (21) QCSDPSubtermProof [EQUIVALENT, 0 ms] (22) QCSDP (23) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (24) TRUE (25) QCSDP (26) QCSDPSubtermProof [EQUIVALENT, 0 ms] (27) QCSDP (28) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: U11(tt, V1, V2) -> U12(isNat(V1), V2) U12(tt, V2) -> U13(isNat(V2)) U13(tt) -> tt U21(tt, V1) -> U22(isNat(V1)) U22(tt) -> tt U31(tt, V1, V2) -> U32(isNat(V1), V2) U32(tt, V2) -> U33(isNat(V2)) U33(tt) -> tt U41(tt, N) -> N U51(tt, M, N) -> s(plus(N, M)) U61(tt) -> 0 U71(tt, M, N) -> plus(x(N, M), N) and(tt, X) -> X isNat(0) -> tt isNat(plus(V1, V2)) -> U11(and(isNatKind(V1), isNatKind(V2)), V1, V2) isNat(s(V1)) -> U21(isNatKind(V1), V1) isNat(x(V1, V2)) -> U31(and(isNatKind(V1), isNatKind(V2)), V1, V2) isNatKind(0) -> tt isNatKind(plus(V1, V2)) -> and(isNatKind(V1), isNatKind(V2)) isNatKind(s(V1)) -> isNatKind(V1) isNatKind(x(V1, V2)) -> and(isNatKind(V1), isNatKind(V2)) plus(N, 0) -> U41(and(isNat(N), isNatKind(N)), N) plus(N, s(M)) -> U51(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) x(N, 0) -> U61(and(isNat(N), isNatKind(N))) x(N, s(M)) -> U71(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) The replacement map contains the following entries: U11: {1} tt: empty set U12: {1} isNat: empty set U13: {1} U21: {1} U22: {1} U31: {1} U32: {1} U33: {1} U41: {1} U51: {1} s: {1} plus: {1, 2} U61: {1} 0: empty set U71: {1} x: {1, 2} and: {1} isNatKind: empty set ---------------------------------------- (1) CSDependencyPairsProof (EQUIVALENT) Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. ---------------------------------------- popout

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all output return to TRS Contextsensitive