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TRS_Contextsensitive 2019-03-21 05.07 pair #429997015
details
property
value
status
complete
benchmark
Ex1_2_Luc02c.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n176.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.45349 seconds
cpu usage
2.9078
user time
2.76714
system time
0.14066
max virtual memory
1.8343352E7
max residence set size
203928.0
stage attributes
key
value
starexec-result
YES
output
2.70/1.41 YES 2.87/1.41 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.87/1.41 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.87/1.41 2.87/1.41 2.87/1.41 Termination of the given CSR could be proven: 2.87/1.41 2.87/1.41 (0) CSR 2.87/1.41 (1) CSRInnermostProof [EQUIVALENT, 0 ms] 2.87/1.41 (2) CSR 2.87/1.41 (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] 2.87/1.41 (4) QCSDP 2.87/1.41 (5) QCSDependencyGraphProof [EQUIVALENT, 0 ms] 2.87/1.41 (6) QCSDP 2.87/1.41 (7) QCSDPSubtermProof [EQUIVALENT, 0 ms] 2.87/1.41 (8) QCSDP 2.87/1.41 (9) PIsEmptyProof [EQUIVALENT, 0 ms] 2.87/1.41 (10) YES 2.87/1.41 2.87/1.41 2.87/1.41 ---------------------------------------- 2.87/1.41 2.87/1.41 (0) 2.87/1.41 Obligation: 2.87/1.41 Context-sensitive rewrite system: 2.87/1.41 The TRS R consists of the following rules: 2.87/1.41 2.87/1.41 2nd(cons(X, cons(Y, Z))) -> Y 2.87/1.41 from(X) -> cons(X, from(s(X))) 2.87/1.41 2.87/1.41 The replacement map contains the following entries: 2.87/1.41 2.87/1.41 2nd: {1} 2.87/1.41 cons: {1} 2.87/1.41 from: {1} 2.87/1.41 s: {1} 2.87/1.41 2.87/1.41 ---------------------------------------- 2.87/1.41 2.87/1.41 (1) CSRInnermostProof (EQUIVALENT) 2.87/1.41 The CSR is orthogonal. By [CS_Inn] we can switch to innermost. 2.87/1.41 ---------------------------------------- 2.87/1.41 2.87/1.41 (2) 2.87/1.41 Obligation: 2.87/1.41 Context-sensitive rewrite system: 2.87/1.41 The TRS R consists of the following rules: 2.87/1.41 2.87/1.41 2nd(cons(X, cons(Y, Z))) -> Y 2.87/1.41 from(X) -> cons(X, from(s(X))) 2.87/1.41 2.87/1.41 The replacement map contains the following entries: 2.87/1.41 2.87/1.41 2nd: {1} 2.87/1.41 cons: {1} 2.87/1.41 from: {1} 2.87/1.41 s: {1} 2.87/1.41 2.87/1.41 2.87/1.41 Innermost Strategy. 2.87/1.41 2.87/1.41 ---------------------------------------- 2.87/1.41 2.87/1.41 (3) CSDependencyPairsProof (EQUIVALENT) 2.87/1.41 Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. 2.87/1.41 ---------------------------------------- 2.87/1.41 2.87/1.41 (4) 2.87/1.41 Obligation: 2.87/1.41 Q-restricted context-sensitive dependency pair problem: 2.87/1.41 The symbols in {2nd_1, from_1, s_1, 2ND_1, FROM_1} are replacing on all positions. 2.87/1.41 For all symbols f in {cons_2} we have mu(f) = {1}. 2.87/1.41 The symbols in {U_1} are not replacing on any position. 2.87/1.41 2.87/1.41 The collapsing dependency pairs are DP_c: 2.87/1.41 2ND(cons(X, cons(Y, Z))) -> Y 2.87/1.41 2.87/1.41 2.87/1.41 The hidden terms of R are: 2.87/1.41 2.87/1.41 from(s(x0)) 2.87/1.41 2.87/1.41 Every hiding context is built from: 2.87/1.41 aprove.DPFramework.CSDPProblem.QCSDPProblem$1@6654e7f5 2.87/1.41 aprove.DPFramework.CSDPProblem.QCSDPProblem$1@5ed0b466 2.87/1.41 2.87/1.41 Hence, the new unhiding pairs DP_u are : 2.87/1.41 2ND(cons(X, cons(Y, Z))) -> U(Y) 2.87/1.41 U(s(x_0)) -> U(x_0) 2.87/1.41 U(from(x_0)) -> U(x_0) 2.87/1.41 U(from(s(x0))) -> FROM(s(x0)) 2.87/1.41 2.87/1.41 The TRS R consists of the following rules: 2.87/1.41 2.87/1.41 2nd(cons(X, cons(Y, Z))) -> Y 2.87/1.41 from(X) -> cons(X, from(s(X))) 2.87/1.41 2.87/1.41 The set Q consists of the following terms: 2.87/1.41 2.87/1.41 2nd(cons(x0, cons(x1, x2)))
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