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TRS Conte Sensi 17651 pair #381733311
details
property
value
status
complete
benchmark
MYNAT_complete-peanoSimple.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
Maude_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.70060610771 seconds
cpu usage
4.531425582
max memory
2.66530816E8
stage attributes
key
value
output-size
16260
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 105 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 16 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 0 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 4 ms] (10) CSR (11) CSRRRRProof [EQUIVALENT, 0 ms] (12) CSR (13) CSRRRRProof [EQUIVALENT, 0 ms] (14) CSR (15) RisEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (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, N) -> N U41(tt, M, N) -> s(plus(N, M)) 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) isNatKind(0) -> tt isNatKind(plus(V1, V2)) -> and(isNatKind(V1), isNatKind(V2)) isNatKind(s(V1)) -> isNatKind(V1) plus(N, 0) -> U31(and(isNat(N), isNatKind(N)), N) plus(N, s(M)) -> U41(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} U41: {1} s: {1} plus: {1, 2} and: {1} 0: empty set isNatKind: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: 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, N) -> N U41(tt, M, N) -> s(plus(N, M)) 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) isNatKind(0) -> tt isNatKind(plus(V1, V2)) -> and(isNatKind(V1), isNatKind(V2)) isNatKind(s(V1)) -> isNatKind(V1) plus(N, 0) -> U31(and(isNat(N), isNatKind(N)), N) plus(N, s(M)) -> U41(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
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