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SRS_Standard 2019-03-29 03.29 pair #432291073
details
property
value
status
complete
benchmark
size-12-alpha-3-num-114.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
15.9504 seconds
cpu usage
58.961
user time
56.9743
system time
1.98671
max virtual memory
1.18687552E8
max residence set size
4537852.0
stage attributes
key
value
starexec-result
YES
output
58.33/15.82 YES 58.33/15.86 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 58.33/15.86 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 58.33/15.86 58.33/15.86 58.33/15.86 Termination w.r.t. Q of the given QTRS could be proven: 58.33/15.86 58.33/15.86 (0) QTRS 58.33/15.86 (1) QTRS Reverse [EQUIVALENT, 0 ms] 58.33/15.86 (2) QTRS 58.33/15.86 (3) DependencyPairsProof [EQUIVALENT, 1 ms] 58.33/15.86 (4) QDP 58.33/15.86 (5) QDPOrderProof [EQUIVALENT, 251 ms] 58.33/15.86 (6) QDP 58.33/15.86 (7) QDPOrderProof [EQUIVALENT, 11 ms] 58.33/15.86 (8) QDP 58.33/15.86 (9) QDPOrderProof [EQUIVALENT, 24 ms] 58.33/15.86 (10) QDP 58.33/15.86 (11) QDPOrderProof [EQUIVALENT, 28 ms] 58.33/15.86 (12) QDP 58.33/15.86 (13) DependencyGraphProof [EQUIVALENT, 0 ms] 58.33/15.86 (14) TRUE 58.33/15.86 58.33/15.86 58.33/15.86 ---------------------------------------- 58.33/15.86 58.33/15.86 (0) 58.33/15.86 Obligation: 58.33/15.86 Q restricted rewrite system: 58.33/15.86 The TRS R consists of the following rules: 58.33/15.86 58.33/15.86 a(x1) -> x1 58.33/15.86 a(a(b(x1))) -> b(c(a(a(a(x1))))) 58.33/15.86 c(a(x1)) -> b(x1) 58.33/15.86 58.33/15.86 Q is empty. 58.33/15.86 58.33/15.86 ---------------------------------------- 58.33/15.86 58.33/15.86 (1) QTRS Reverse (EQUIVALENT) 58.33/15.86 We applied the QTRS Reverse Processor [REVERSE]. 58.33/15.86 ---------------------------------------- 58.33/15.86 58.33/15.86 (2) 58.33/15.86 Obligation: 58.33/15.86 Q restricted rewrite system: 58.33/15.86 The TRS R consists of the following rules: 58.33/15.86 58.33/15.86 a(x1) -> x1 58.33/15.86 b(a(a(x1))) -> a(a(a(c(b(x1))))) 58.33/15.86 a(c(x1)) -> b(x1) 58.33/15.86 58.33/15.86 Q is empty. 58.33/15.86 58.33/15.86 ---------------------------------------- 58.33/15.86 58.33/15.86 (3) DependencyPairsProof (EQUIVALENT) 58.33/15.86 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 58.33/15.86 ---------------------------------------- 58.33/15.86 58.33/15.86 (4) 58.33/15.86 Obligation: 58.33/15.86 Q DP problem: 58.33/15.86 The TRS P consists of the following rules: 58.33/15.86 58.33/15.86 B(a(a(x1))) -> A(a(a(c(b(x1))))) 58.33/15.86 B(a(a(x1))) -> A(a(c(b(x1)))) 58.33/15.86 B(a(a(x1))) -> A(c(b(x1))) 58.33/15.86 B(a(a(x1))) -> B(x1) 58.33/15.86 A(c(x1)) -> B(x1) 58.33/15.86 58.33/15.86 The TRS R consists of the following rules: 58.33/15.86 58.33/15.86 a(x1) -> x1 58.33/15.86 b(a(a(x1))) -> a(a(a(c(b(x1))))) 58.33/15.86 a(c(x1)) -> b(x1) 58.33/15.86 58.33/15.86 Q is empty. 58.33/15.86 We have to consider all minimal (P,Q,R)-chains. 58.33/15.86 ---------------------------------------- 58.33/15.86 58.33/15.86 (5) QDPOrderProof (EQUIVALENT) 58.33/15.86 We use the reduction pair processor [LPAR04,JAR06]. 58.33/15.86 58.33/15.86 58.33/15.86 The following pairs can be oriented strictly and are deleted. 58.33/15.86 58.33/15.86 B(a(a(x1))) -> B(x1) 58.33/15.86 The remaining pairs can at least be oriented weakly. 58.33/15.86 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 58.33/15.86 58.33/15.86 <<< 58.33/15.86 POL(B(x_1)) = [[0A]] + [[-I, 0A, -I]] * x_1 58.33/15.86 >>> 58.33/15.86 58.33/15.86 <<< 58.33/15.86 POL(a(x_1)) = [[0A], [-I], [1A]] + [[0A, 0A, -I], [0A, 0A, 0A], [-I, 1A, 0A]] * x_1 58.33/15.86 >>> 58.33/15.86 58.33/15.86 <<<
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