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SRS_Standard 2019-03-29 03.29 pair #432289741
details
property
value
status
complete
benchmark
size-12-alpha-3-num-551.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
7.75671 seconds
cpu usage
26.9873
user time
25.7907
system time
1.19664
max virtual memory
1.03559284E8
max residence set size
3183276.0
stage attributes
key
value
starexec-result
YES
output
25.63/7.41 YES 26.70/7.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 26.70/7.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 26.70/7.67 26.70/7.67 26.70/7.67 Termination w.r.t. Q of the given QTRS could be proven: 26.70/7.67 26.70/7.67 (0) QTRS 26.70/7.67 (1) DependencyPairsProof [EQUIVALENT, 27 ms] 26.70/7.67 (2) QDP 26.70/7.67 (3) QDPOrderProof [EQUIVALENT, 107 ms] 26.70/7.67 (4) QDP 26.70/7.67 (5) PisEmptyProof [EQUIVALENT, 0 ms] 26.70/7.67 (6) YES 26.70/7.67 26.70/7.67 26.70/7.67 ---------------------------------------- 26.70/7.67 26.70/7.67 (0) 26.70/7.67 Obligation: 26.70/7.67 Q restricted rewrite system: 26.70/7.67 The TRS R consists of the following rules: 26.70/7.67 26.70/7.67 a(b(x1)) -> x1 26.70/7.67 a(c(x1)) -> b(c(c(a(x1)))) 26.70/7.67 b(c(x1)) -> a(b(x1)) 26.70/7.67 26.70/7.67 Q is empty. 26.70/7.67 26.70/7.67 ---------------------------------------- 26.70/7.67 26.70/7.67 (1) DependencyPairsProof (EQUIVALENT) 26.70/7.67 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 26.70/7.67 ---------------------------------------- 26.70/7.67 26.70/7.67 (2) 26.70/7.67 Obligation: 26.70/7.67 Q DP problem: 26.70/7.67 The TRS P consists of the following rules: 26.70/7.67 26.70/7.67 A(c(x1)) -> B(c(c(a(x1)))) 26.70/7.67 A(c(x1)) -> A(x1) 26.70/7.67 B(c(x1)) -> A(b(x1)) 26.70/7.67 B(c(x1)) -> B(x1) 26.70/7.67 26.70/7.67 The TRS R consists of the following rules: 26.70/7.67 26.70/7.67 a(b(x1)) -> x1 26.70/7.67 a(c(x1)) -> b(c(c(a(x1)))) 26.70/7.67 b(c(x1)) -> a(b(x1)) 26.70/7.67 26.70/7.67 Q is empty. 26.70/7.67 We have to consider all minimal (P,Q,R)-chains. 26.70/7.67 ---------------------------------------- 26.70/7.67 26.70/7.67 (3) QDPOrderProof (EQUIVALENT) 26.70/7.67 We use the reduction pair processor [LPAR04,JAR06]. 26.70/7.67 26.70/7.67 26.70/7.67 The following pairs can be oriented strictly and are deleted. 26.70/7.67 26.70/7.67 A(c(x1)) -> B(c(c(a(x1)))) 26.70/7.67 A(c(x1)) -> A(x1) 26.70/7.67 B(c(x1)) -> A(b(x1)) 26.70/7.67 B(c(x1)) -> B(x1) 26.70/7.67 The remaining pairs can at least be oriented weakly. 26.70/7.67 Used ordering: Polynomial interpretation [POLO,RATPOLO]: 26.70/7.67 26.70/7.67 POL(A(x_1)) = [7/4] + [2]x_1 26.70/7.67 POL(B(x_1)) = [1/2]x_1 26.70/7.67 POL(a(x_1)) = [3/2] + [2]x_1 26.70/7.67 POL(b(x_1)) = [1/2]x_1 26.70/7.67 POL(c(x_1)) = [4] + [2]x_1 26.70/7.67 The value of delta used in the strict ordering is 1/4. 26.70/7.67 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 26.70/7.67 26.70/7.67 a(b(x1)) -> x1 26.70/7.67 a(c(x1)) -> b(c(c(a(x1)))) 26.70/7.67 b(c(x1)) -> a(b(x1)) 26.70/7.67 26.70/7.67 26.70/7.67 ---------------------------------------- 26.70/7.67 26.70/7.67 (4) 26.70/7.67 Obligation: 26.70/7.67 Q DP problem: 26.70/7.67 P is empty. 26.70/7.67 The TRS R consists of the following rules: 26.70/7.67 26.70/7.67 a(b(x1)) -> x1 26.70/7.67 a(c(x1)) -> b(c(c(a(x1)))) 26.70/7.67 b(c(x1)) -> a(b(x1)) 26.70/7.67 26.70/7.67 Q is empty. 26.70/7.67 We have to consider all minimal (P,Q,R)-chains. 26.70/7.67 ---------------------------------------- 26.70/7.67 26.70/7.67 (5) PisEmptyProof (EQUIVALENT) 26.70/7.67 The TRS P is empty. Hence, there is no (P,Q,R) chain. 26.70/7.67 ----------------------------------------
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