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SRS_Standard 2019-03-29 03.29 pair #432290605
details
property
value
status
complete
benchmark
size-12-alpha-3-num-15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n095.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
8.58423 seconds
cpu usage
30.1954
user time
28.8947
system time
1.30074
max virtual memory
8.2092404E7
max residence set size
3793596.0
stage attributes
key
value
starexec-result
YES
output
29.39/8.44 YES 29.79/8.47 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 29.79/8.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 29.79/8.47 29.79/8.47 29.79/8.47 Termination w.r.t. Q of the given QTRS could be proven: 29.79/8.47 29.79/8.47 (0) QTRS 29.79/8.47 (1) DependencyPairsProof [EQUIVALENT, 8 ms] 29.79/8.47 (2) QDP 29.79/8.47 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 29.79/8.47 (4) QDP 29.79/8.47 (5) QDPOrderProof [EQUIVALENT, 119 ms] 29.79/8.47 (6) QDP 29.79/8.47 (7) QDPOrderProof [EQUIVALENT, 0 ms] 29.79/8.47 (8) QDP 29.79/8.47 (9) PisEmptyProof [EQUIVALENT, 0 ms] 29.79/8.47 (10) YES 29.79/8.47 29.79/8.47 29.79/8.47 ---------------------------------------- 29.79/8.47 29.79/8.47 (0) 29.79/8.47 Obligation: 29.79/8.47 Q restricted rewrite system: 29.79/8.47 The TRS R consists of the following rules: 29.79/8.47 29.79/8.47 a(x1) -> x1 29.79/8.47 a(x1) -> b(x1) 29.79/8.47 a(c(b(x1))) -> c(c(a(a(x1)))) 29.79/8.47 c(x1) -> b(x1) 29.79/8.47 29.79/8.47 Q is empty. 29.79/8.47 29.79/8.47 ---------------------------------------- 29.79/8.47 29.79/8.47 (1) DependencyPairsProof (EQUIVALENT) 29.79/8.47 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 29.79/8.47 ---------------------------------------- 29.79/8.47 29.79/8.47 (2) 29.79/8.47 Obligation: 29.79/8.47 Q DP problem: 29.79/8.47 The TRS P consists of the following rules: 29.79/8.47 29.79/8.47 A(c(b(x1))) -> C(c(a(a(x1)))) 29.79/8.47 A(c(b(x1))) -> C(a(a(x1))) 29.79/8.48 A(c(b(x1))) -> A(a(x1)) 29.79/8.48 A(c(b(x1))) -> A(x1) 29.79/8.48 29.79/8.48 The TRS R consists of the following rules: 29.79/8.48 29.79/8.48 a(x1) -> x1 29.79/8.48 a(x1) -> b(x1) 29.79/8.48 a(c(b(x1))) -> c(c(a(a(x1)))) 29.79/8.48 c(x1) -> b(x1) 29.79/8.48 29.79/8.48 Q is empty. 29.79/8.48 We have to consider all minimal (P,Q,R)-chains. 29.79/8.48 ---------------------------------------- 29.79/8.48 29.79/8.48 (3) DependencyGraphProof (EQUIVALENT) 29.79/8.48 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 29.79/8.48 ---------------------------------------- 29.79/8.48 29.79/8.48 (4) 29.79/8.48 Obligation: 29.79/8.48 Q DP problem: 29.79/8.48 The TRS P consists of the following rules: 29.79/8.48 29.79/8.48 A(c(b(x1))) -> A(x1) 29.79/8.48 A(c(b(x1))) -> A(a(x1)) 29.79/8.48 29.79/8.48 The TRS R consists of the following rules: 29.79/8.48 29.79/8.48 a(x1) -> x1 29.79/8.48 a(x1) -> b(x1) 29.79/8.48 a(c(b(x1))) -> c(c(a(a(x1)))) 29.79/8.48 c(x1) -> b(x1) 29.79/8.48 29.79/8.48 Q is empty. 29.79/8.48 We have to consider all minimal (P,Q,R)-chains. 29.79/8.48 ---------------------------------------- 29.79/8.48 29.79/8.48 (5) QDPOrderProof (EQUIVALENT) 29.79/8.48 We use the reduction pair processor [LPAR04,JAR06]. 29.79/8.48 29.79/8.48 29.79/8.48 The following pairs can be oriented strictly and are deleted. 29.79/8.48 29.79/8.48 A(c(b(x1))) -> A(x1) 29.79/8.48 The remaining pairs can at least be oriented weakly. 29.79/8.48 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 29.79/8.48 29.79/8.48 <<< 29.79/8.48 POL(A(x_1)) = [[0A]] + [[0A, 1A, 0A]] * x_1 29.79/8.48 >>> 29.79/8.48 29.79/8.48 <<< 29.79/8.48 POL(c(x_1)) = [[-I], [-I], [1A]] + [[0A, 0A, 0A], [1A, 0A, 0A], [-I, -I, 0A]] * x_1
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