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TRS Context Sensitive pair #516978909
details
property
value
status
complete
benchmark
MYNAT_nosorts.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n114.star.cs.uiowa.edu
space
Maude_06
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
1.94422411919 seconds
cpu usage
5.167760363
max memory
4.72920064E8
stage attributes
key
value
output-size
6645
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be proven: (0) CSR (1) CSRInnermostProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] (4) QCSDP (5) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QCSDP (8) QCSDPSubtermProof [EQUIVALENT, 0 ms] (9) QCSDP (10) PIsEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) QCSDP (13) QCSDPSubtermProof [EQUIVALENT, 0 ms] (14) QCSDP (15) PIsEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: and(tt, X) -> X plus(N, 0) -> N plus(N, s(M)) -> s(plus(N, M)) x(N, 0) -> 0 x(N, s(M)) -> plus(x(N, M), N) The replacement map contains the following entries: and: {1} tt: empty set plus: {1, 2} 0: empty set s: {1} x: {1, 2} ---------------------------------------- (1) CSRInnermostProof (EQUIVALENT) The CSR is orthogonal. By [CS_Inn] we can switch to innermost. ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: and(tt, X) -> X plus(N, 0) -> N plus(N, s(M)) -> s(plus(N, M)) x(N, 0) -> 0 x(N, s(M)) -> plus(x(N, M), N) The replacement map contains the following entries: and: {1} tt: empty set plus: {1, 2} 0: empty set s: {1} x: {1, 2} Innermost Strategy. ---------------------------------------- (3) CSDependencyPairsProof (EQUIVALENT) Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. ---------------------------------------- (4) Obligation: Q-restricted context-sensitive dependency pair problem: The symbols in {plus_2, s_1, x_2, PLUS_2, X_2} are replacing on all positions. For all symbols f in {and_2, AND_2} we have mu(f) = {1}. The symbols in {U_1} are not replacing on any position. The ordinary context-sensitive dependency pairs DP_o are: PLUS(N, s(M)) -> PLUS(N, M) X(N, s(M)) -> PLUS(x(N, M), N) X(N, s(M)) -> X(N, M)
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