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SRS_Standard 2019-03-29 03.29 pair #432290857
details
property
value
status
complete
benchmark
size-12-alpha-3-num-304.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
11.5227 seconds
cpu usage
40.904
user time
39.2847
system time
1.61921
max virtual memory
1.04644916E8
max residence set size
4425280.0
stage attributes
key
value
starexec-result
YES
output
40.39/11.32 YES 40.47/11.34 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 40.47/11.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 40.47/11.34 40.47/11.34 40.47/11.34 Termination w.r.t. Q of the given QTRS could be proven: 40.47/11.34 40.47/11.34 (0) QTRS 40.47/11.34 (1) DependencyPairsProof [EQUIVALENT, 20 ms] 40.47/11.34 (2) QDP 40.47/11.34 (3) DependencyGraphProof [EQUIVALENT, 4 ms] 40.47/11.34 (4) QDP 40.47/11.34 (5) QDPOrderProof [EQUIVALENT, 140 ms] 40.47/11.34 (6) QDP 40.47/11.34 (7) QDPOrderProof [EQUIVALENT, 44 ms] 40.47/11.34 (8) QDP 40.47/11.34 (9) PisEmptyProof [EQUIVALENT, 0 ms] 40.47/11.34 (10) YES 40.47/11.34 40.47/11.34 40.47/11.34 ---------------------------------------- 40.47/11.34 40.47/11.34 (0) 40.47/11.34 Obligation: 40.47/11.34 Q restricted rewrite system: 40.47/11.34 The TRS R consists of the following rules: 40.47/11.34 40.47/11.34 a(x1) -> x1 40.47/11.34 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 40.47/11.34 c(b(x1)) -> x1 40.47/11.34 40.47/11.34 Q is empty. 40.47/11.34 40.47/11.34 ---------------------------------------- 40.47/11.34 40.47/11.34 (1) DependencyPairsProof (EQUIVALENT) 40.47/11.34 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 40.47/11.34 ---------------------------------------- 40.47/11.34 40.47/11.34 (2) 40.47/11.34 Obligation: 40.47/11.34 Q DP problem: 40.47/11.34 The TRS P consists of the following rules: 40.47/11.34 40.47/11.34 A(b(b(x1))) -> C(a(a(x1))) 40.47/11.34 A(b(b(x1))) -> A(a(x1)) 40.47/11.34 A(b(b(x1))) -> A(x1) 40.47/11.34 40.47/11.34 The TRS R consists of the following rules: 40.47/11.34 40.47/11.34 a(x1) -> x1 40.47/11.34 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 40.47/11.34 c(b(x1)) -> x1 40.47/11.34 40.47/11.34 Q is empty. 40.47/11.34 We have to consider all minimal (P,Q,R)-chains. 40.47/11.34 ---------------------------------------- 40.47/11.34 40.47/11.34 (3) DependencyGraphProof (EQUIVALENT) 40.47/11.34 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 40.47/11.34 ---------------------------------------- 40.47/11.34 40.47/11.34 (4) 40.47/11.34 Obligation: 40.47/11.34 Q DP problem: 40.47/11.34 The TRS P consists of the following rules: 40.47/11.34 40.47/11.34 A(b(b(x1))) -> A(x1) 40.47/11.34 A(b(b(x1))) -> A(a(x1)) 40.47/11.34 40.47/11.34 The TRS R consists of the following rules: 40.47/11.34 40.47/11.34 a(x1) -> x1 40.47/11.34 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 40.47/11.34 c(b(x1)) -> x1 40.47/11.34 40.47/11.34 Q is empty. 40.47/11.34 We have to consider all minimal (P,Q,R)-chains. 40.47/11.34 ---------------------------------------- 40.47/11.34 40.47/11.34 (5) QDPOrderProof (EQUIVALENT) 40.47/11.34 We use the reduction pair processor [LPAR04,JAR06]. 40.47/11.34 40.47/11.34 40.47/11.34 The following pairs can be oriented strictly and are deleted. 40.47/11.34 40.47/11.34 A(b(b(x1))) -> A(x1) 40.47/11.34 The remaining pairs can at least be oriented weakly. 40.47/11.34 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 40.47/11.34 40.47/11.34 <<< 40.47/11.34 POL(A(x_1)) = [[0A]] + [[0A, 0A, -I]] * x_1 40.47/11.34 >>> 40.47/11.34 40.47/11.34 <<< 40.47/11.34 POL(b(x_1)) = [[0A], [1A], [-I]] + [[0A, 0A, -I], [1A, 0A, 0A], [0A, -I, 0A]] * x_1 40.47/11.34 >>> 40.47/11.34 40.47/11.34 <<< 40.47/11.34 POL(a(x_1)) = [[-I], [-I], [0A]] + [[0A, -I, -I], [1A, 0A, 0A], [-I, 0A, 0A]] * x_1
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