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TRS Conte Sensi 17651 pair #381733251
details
property
value
status
complete
benchmark
MYNAT_nokinds-noand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Maude_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.67395401001 seconds
cpu usage
4.046055953
max memory
2.238464E8
stage attributes
key
value
output-size
14256
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSDependencyPairsProof [EQUIVALENT, 46 ms] (2) QCSDP (3) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QCSDP (6) QCSDPSubtermProof [EQUIVALENT, 0 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, V2) -> U12(isNat(V2)) U12(tt) -> tt U21(tt) -> tt U31(tt, V2) -> U32(isNat(V2)) U32(tt) -> tt U41(tt, N) -> N U51(tt, M, N) -> U52(isNat(N), M, N) U52(tt, M, N) -> s(plus(N, M)) U61(tt) -> 0 U71(tt, M, N) -> U72(isNat(N), M, N) U72(tt, M, N) -> plus(x(N, M), N) isNat(0) -> tt isNat(plus(V1, V2)) -> U11(isNat(V1), V2) isNat(s(V1)) -> U21(isNat(V1)) isNat(x(V1, V2)) -> U31(isNat(V1), V2) plus(N, 0) -> U41(isNat(N), N) plus(N, s(M)) -> U51(isNat(M), M, N) x(N, 0) -> U61(isNat(N)) x(N, s(M)) -> U71(isNat(M), M, N) The replacement map contains the following entries: U11: {1} tt: empty set U12: {1} isNat: empty set U21: {1} U31: {1} U32: {1} U41: {1} U51: {1} U52: {1} s: {1} plus: {1, 2} U61: {1} 0: empty set U71: {1} U72: {1} x: {1, 2} ---------------------------------------- (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 {U12_1, U21_1, U32_1, s_1, plus_2, U61_1, x_2, U12'_1, U32'_1, PLUS_2, X_2, U21'_1, U61'_1} are replacing on all positions. For all symbols f in {U11_2, U31_2, U41_2, U51_3, U52_3, U71_3, U72_3, U11'_2, U31'_2, U52'_3, U51'_3, U72'_3, U71'_3, U41'_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: U11'(tt, V2) -> U12'(isNat(V2)) U11'(tt, V2) -> ISNAT(V2) U31'(tt, V2) -> U32'(isNat(V2)) U31'(tt, V2) -> ISNAT(V2)
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