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SRS_Standard 2019-03-29 03.29 pair #432291307
details
property
value
status
complete
benchmark
size-12-alpha-3-num-472.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
11.9748 seconds
cpu usage
42.8805
user time
41.1089
system time
1.77165
max virtual memory
5.9443612E7
max residence set size
3999464.0
stage attributes
key
value
starexec-result
YES
output
42.39/11.78 YES 42.39/11.82 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 42.39/11.82 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 42.39/11.82 42.39/11.82 42.39/11.82 Termination w.r.t. Q of the given QTRS could be proven: 42.39/11.82 42.39/11.82 (0) QTRS 42.39/11.82 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 42.39/11.82 (2) QDP 42.39/11.82 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 42.39/11.82 (4) QDP 42.39/11.82 (5) QDPOrderProof [EQUIVALENT, 341 ms] 42.39/11.82 (6) QDP 42.39/11.82 (7) UsableRulesProof [EQUIVALENT, 0 ms] 42.39/11.82 (8) QDP 42.39/11.82 (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] 42.39/11.82 (10) YES 42.39/11.82 42.39/11.82 42.39/11.82 ---------------------------------------- 42.39/11.82 42.39/11.82 (0) 42.39/11.82 Obligation: 42.39/11.82 Q restricted rewrite system: 42.39/11.82 The TRS R consists of the following rules: 42.39/11.82 42.39/11.82 a(a(x1)) -> x1 42.39/11.82 b(b(x1)) -> c(c(c(x1))) 42.39/11.82 b(c(x1)) -> a(b(b(x1))) 42.39/11.82 42.39/11.82 Q is empty. 42.39/11.82 42.39/11.82 ---------------------------------------- 42.39/11.82 42.39/11.82 (1) DependencyPairsProof (EQUIVALENT) 42.39/11.82 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 42.39/11.82 ---------------------------------------- 42.39/11.82 42.39/11.82 (2) 42.39/11.82 Obligation: 42.39/11.82 Q DP problem: 42.39/11.82 The TRS P consists of the following rules: 42.39/11.82 42.39/11.82 B(c(x1)) -> A(b(b(x1))) 42.39/11.82 B(c(x1)) -> B(b(x1)) 42.39/11.82 B(c(x1)) -> B(x1) 42.39/11.82 42.39/11.82 The TRS R consists of the following rules: 42.39/11.82 42.39/11.82 a(a(x1)) -> x1 42.39/11.82 b(b(x1)) -> c(c(c(x1))) 42.39/11.82 b(c(x1)) -> a(b(b(x1))) 42.39/11.82 42.39/11.82 Q is empty. 42.39/11.82 We have to consider all minimal (P,Q,R)-chains. 42.39/11.82 ---------------------------------------- 42.39/11.82 42.39/11.82 (3) DependencyGraphProof (EQUIVALENT) 42.39/11.82 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 42.39/11.82 ---------------------------------------- 42.39/11.82 42.39/11.82 (4) 42.39/11.82 Obligation: 42.39/11.82 Q DP problem: 42.39/11.82 The TRS P consists of the following rules: 42.39/11.82 42.39/11.82 B(c(x1)) -> B(x1) 42.39/11.82 B(c(x1)) -> B(b(x1)) 42.39/11.82 42.39/11.82 The TRS R consists of the following rules: 42.39/11.82 42.39/11.82 a(a(x1)) -> x1 42.39/11.82 b(b(x1)) -> c(c(c(x1))) 42.39/11.82 b(c(x1)) -> a(b(b(x1))) 42.39/11.82 42.39/11.82 Q is empty. 42.39/11.82 We have to consider all minimal (P,Q,R)-chains. 42.39/11.82 ---------------------------------------- 42.39/11.82 42.39/11.82 (5) QDPOrderProof (EQUIVALENT) 42.39/11.82 We use the reduction pair processor [LPAR04,JAR06]. 42.39/11.82 42.39/11.82 42.39/11.82 The following pairs can be oriented strictly and are deleted. 42.39/11.82 42.39/11.82 B(c(x1)) -> B(b(x1)) 42.39/11.82 The remaining pairs can at least be oriented weakly. 42.39/11.82 Used ordering: Matrix interpretation [MATRO] with arctic integers [ARCTIC,STERNAGEL_THIEMANN_RTA14]: 42.39/11.82 42.39/11.82 <<< 42.39/11.82 POL(B(x_1)) = [[0A]] + [[-1A, -1A, -1A]] * x_1 42.39/11.82 >>> 42.39/11.82 42.39/11.82 <<< 42.39/11.82 POL(c(x_1)) = [[2A], [-I], [0A]] + [[0A, -1A, 0A], [-I, -1A, -I], [-I, 2A, -I]] * x_1 42.39/11.82 >>> 42.39/11.82 42.39/11.82 <<< 42.39/11.82 POL(b(x_1)) = [[0A], [1A], [-I]] + [[-1A, 1A, -1A], [-1A, 1A, -1A], [-1A, -1A, -1A]] * x_1
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