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TRS Conte Sensi 17651 pair #381733378
details
property
value
status
complete
benchmark
MYNAT_nokinds.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n105.star.cs.uiowa.edu
space
Maude_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.14711594582 seconds
cpu usage
5.731696599
max memory
3.84663552E8
stage attributes
key
value
output-size
13133
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSDependencyPairsProof [EQUIVALENT, 0 ms] (2) QCSDP (3) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QCSDP (6) QCSDPReductionPairProof [EQUIVALENT, 93 ms] (7) QCSDP (8) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (9) TRUE (10) QCSDP (11) QCSDPSubtermProof [EQUIVALENT, 0 ms] (12) QCSDP (13) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE (15) QCSDP (16) QCSDPSubtermProof [EQUIVALENT, 0 ms] (17) QCSDP (18) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (19) TRUE ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: U11(tt, N) -> N U21(tt, M, N) -> s(plus(N, M)) U31(tt) -> 0 U41(tt, M, N) -> plus(x(N, M), N) and(tt, X) -> X isNat(0) -> tt isNat(plus(V1, V2)) -> and(isNat(V1), isNat(V2)) isNat(s(V1)) -> isNat(V1) isNat(x(V1, V2)) -> and(isNat(V1), isNat(V2)) plus(N, 0) -> U11(isNat(N), N) plus(N, s(M)) -> U21(and(isNat(M), isNat(N)), M, N) x(N, 0) -> U31(isNat(N)) x(N, s(M)) -> U41(and(isNat(M), isNat(N)), M, N) The replacement map contains the following entries: U11: {1} tt: empty set U21: {1} s: {1} plus: {1, 2} U31: {1} 0: empty set U41: {1} x: {1, 2} and: {1} isNat: empty set ---------------------------------------- (1) CSDependencyPairsProof (EQUIVALENT) Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. ---------------------------------------- (2) Obligation: Q-restricted context-sensitive dependency pair problem: The symbols in {s_1, plus_2, U31_1, x_2, PLUS_2, X_2, U31'_1} are replacing on all positions. For all symbols f in {U11_2, U21_3, U41_3, and_2, U21'_3, U41'_3, AND_2, U11'_2} we have mu(f) = {1}. The symbols in {isNat_1, ISNAT_1, U_1} are not replacing on any position. The ordinary context-sensitive dependency pairs DP_o are: U21'(tt, M, N) -> PLUS(N, M) U41'(tt, M, N) -> PLUS(x(N, M), N) U41'(tt, M, N) -> X(N, M) ISNAT(plus(V1, V2)) -> AND(isNat(V1), isNat(V2)) ISNAT(plus(V1, V2)) -> ISNAT(V1) ISNAT(s(V1)) -> ISNAT(V1) ISNAT(x(V1, V2)) -> AND(isNat(V1), isNat(V2)) ISNAT(x(V1, V2)) -> ISNAT(V1) PLUS(N, 0) -> U11'(isNat(N), N) PLUS(N, 0) -> ISNAT(N) PLUS(N, s(M)) -> U21'(and(isNat(M), isNat(N)), M, N) PLUS(N, s(M)) -> AND(isNat(M), isNat(N)) PLUS(N, s(M)) -> ISNAT(M) X(N, 0) -> U31'(isNat(N)) X(N, 0) -> ISNAT(N) X(N, s(M)) -> U41'(and(isNat(M), isNat(N)), M, N)
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