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TRS Context Sensitive pair #516978815
details
property
value
status
complete
benchmark
Ex4_7_56_Bor03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n002.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
1.90950608253 seconds
cpu usage
5.305568162
max memory
4.78052352E8
stage attributes
key
value
output-size
6707
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be proven: (0) CSR (1) CSRInnermostProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] (4) QCSDP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: from(X) -> cons(X, from(s(X))) after(0, XS) -> XS after(s(N), cons(X, XS)) -> after(N, XS) The replacement map contains the following entries: from: {1} cons: {1} s: {1} after: {1, 2} 0: empty set ---------------------------------------- (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: from(X) -> cons(X, from(s(X))) after(0, XS) -> XS after(s(N), cons(X, XS)) -> after(N, XS) The replacement map contains the following entries: from: {1} cons: {1} s: {1} after: {1, 2} 0: empty set 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 {from_1, s_1, after_2, AFTER_2, FROM_1} are replacing on all positions. For all symbols f in {cons_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: AFTER(s(N), cons(X, XS)) -> AFTER(N, XS) The collapsing dependency pairs are DP_c: AFTER(s(N), cons(X, XS)) -> XS The hidden terms of R are: from(s(x0))
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