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SRS_Standard 2019-03-29 03.29 pair #432290539
details
property
value
status
complete
benchmark
size-12-alpha-3-num-297.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
10.8686 seconds
cpu usage
34.2118
user time
32.7295
system time
1.48232
max virtual memory
4.0169792E7
max residence set size
4002660.0
stage attributes
key
value
starexec-result
YES
output
31.69/9.03 YES 33.77/9.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 33.77/9.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 33.77/9.58 33.77/9.58 33.77/9.58 Termination w.r.t. Q of the given QTRS could be proven: 33.77/9.58 33.77/9.58 (0) QTRS 33.77/9.58 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 33.77/9.58 (2) QDP 33.77/9.58 (3) QDPOrderProof [EQUIVALENT, 140 ms] 33.77/9.58 (4) QDP 33.77/9.58 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 33.77/9.58 (6) QDP 33.77/9.58 (7) QDPOrderProof [EQUIVALENT, 58 ms] 33.77/9.58 (8) QDP 33.77/9.58 (9) PisEmptyProof [EQUIVALENT, 0 ms] 33.77/9.58 (10) YES 33.77/9.58 33.77/9.58 33.77/9.58 ---------------------------------------- 33.77/9.58 33.77/9.58 (0) 33.77/9.58 Obligation: 33.77/9.58 Q restricted rewrite system: 33.77/9.58 The TRS R consists of the following rules: 33.77/9.58 33.77/9.58 a(x1) -> x1 33.77/9.58 a(b(b(x1))) -> b(b(b(a(c(x1))))) 33.77/9.58 c(b(x1)) -> a(x1) 33.77/9.58 33.77/9.58 Q is empty. 33.77/9.58 33.77/9.58 ---------------------------------------- 33.77/9.58 33.77/9.58 (1) DependencyPairsProof (EQUIVALENT) 33.77/9.58 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 33.77/9.58 ---------------------------------------- 33.77/9.58 33.77/9.58 (2) 33.77/9.58 Obligation: 33.77/9.58 Q DP problem: 33.77/9.58 The TRS P consists of the following rules: 33.77/9.58 33.77/9.58 A(b(b(x1))) -> A(c(x1)) 33.77/9.58 A(b(b(x1))) -> C(x1) 33.77/9.58 C(b(x1)) -> A(x1) 33.77/9.58 33.77/9.58 The TRS R consists of the following rules: 33.77/9.58 33.77/9.58 a(x1) -> x1 33.77/9.58 a(b(b(x1))) -> b(b(b(a(c(x1))))) 33.77/9.58 c(b(x1)) -> a(x1) 33.77/9.58 33.77/9.58 Q is empty. 33.77/9.58 We have to consider all minimal (P,Q,R)-chains. 33.77/9.58 ---------------------------------------- 33.77/9.58 33.77/9.58 (3) QDPOrderProof (EQUIVALENT) 33.77/9.58 We use the reduction pair processor [LPAR04,JAR06]. 33.77/9.58 33.77/9.58 33.77/9.58 The following pairs can be oriented strictly and are deleted. 33.77/9.58 33.77/9.58 A(b(b(x1))) -> C(x1) 33.77/9.58 The remaining pairs can at least be oriented weakly. 33.77/9.58 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 33.77/9.58 33.77/9.58 <<< 33.77/9.58 POL(A(x_1)) = [[-I]] + [[0A, 0A, -I]] * x_1 33.77/9.58 >>> 33.77/9.58 33.77/9.58 <<< 33.77/9.58 POL(b(x_1)) = [[-I], [-I], [0A]] + [[0A, 0A, -I], [0A, -I, 0A], [1A, 0A, 0A]] * x_1 33.77/9.58 >>> 33.77/9.58 33.77/9.58 <<< 33.77/9.58 POL(c(x_1)) = [[-I], [-I], [-I]] + [[0A, 0A, -I], [0A, 0A, -I], [0A, 0A, -I]] * x_1 33.77/9.58 >>> 33.77/9.58 33.77/9.58 <<< 33.77/9.58 POL(C(x_1)) = [[-I]] + [[0A, -I, -I]] * x_1 33.77/9.58 >>> 33.77/9.58 33.77/9.58 <<< 33.77/9.58 POL(a(x_1)) = [[-I], [-I], [-I]] + [[0A, 0A, 0A], [0A, 0A, 0A], [0A, 0A, 0A]] * x_1 33.77/9.58 >>> 33.77/9.58 33.77/9.58 33.77/9.58 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 33.77/9.58 33.77/9.58 c(b(x1)) -> a(x1) 33.77/9.58 a(b(b(x1))) -> b(b(b(a(c(x1))))) 33.77/9.58 a(x1) -> x1 33.77/9.58 33.77/9.58 33.77/9.58 ---------------------------------------- 33.77/9.58 33.77/9.58 (4) 33.77/9.58 Obligation:
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