Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
SRS_Standard 2019-03-29 03.29 pair #432289957
details
property
value
status
complete
benchmark
size-12-alpha-3-num-451.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n032.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.09651 seconds
cpu usage
12.2097
user time
11.4756
system time
0.73407
max virtual memory
1.9875E7
max residence set size
2106152.0
stage attributes
key
value
starexec-result
YES
output
11.93/4.01 YES 11.93/4.03 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.93/4.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.93/4.03 11.93/4.03 11.93/4.03 Termination w.r.t. Q of the given QTRS could be proven: 11.93/4.03 11.93/4.03 (0) QTRS 11.93/4.03 (1) DependencyPairsProof [EQUIVALENT, 2 ms] 11.93/4.03 (2) QDP 11.93/4.03 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 11.93/4.03 (4) QDP 11.93/4.03 (5) QDPOrderProof [EQUIVALENT, 61 ms] 11.93/4.03 (6) QDP 11.93/4.03 (7) PisEmptyProof [EQUIVALENT, 0 ms] 11.93/4.03 (8) YES 11.93/4.03 11.93/4.03 11.93/4.03 ---------------------------------------- 11.93/4.03 11.93/4.03 (0) 11.93/4.03 Obligation: 11.93/4.03 Q restricted rewrite system: 11.93/4.03 The TRS R consists of the following rules: 11.93/4.03 11.93/4.03 a(x1) -> b(c(x1)) 11.93/4.03 a(c(b(x1))) -> b(a(a(c(x1)))) 11.93/4.03 b(b(x1)) -> x1 11.93/4.03 11.93/4.03 Q is empty. 11.93/4.03 11.93/4.03 ---------------------------------------- 11.93/4.03 11.93/4.03 (1) DependencyPairsProof (EQUIVALENT) 11.93/4.03 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 11.93/4.03 ---------------------------------------- 11.93/4.03 11.93/4.03 (2) 11.93/4.03 Obligation: 11.93/4.03 Q DP problem: 11.93/4.03 The TRS P consists of the following rules: 11.93/4.03 11.93/4.03 A(x1) -> B(c(x1)) 11.93/4.03 A(c(b(x1))) -> B(a(a(c(x1)))) 11.93/4.03 A(c(b(x1))) -> A(a(c(x1))) 11.93/4.03 A(c(b(x1))) -> A(c(x1)) 11.93/4.03 11.93/4.03 The TRS R consists of the following rules: 11.93/4.03 11.93/4.03 a(x1) -> b(c(x1)) 11.93/4.03 a(c(b(x1))) -> b(a(a(c(x1)))) 11.93/4.03 b(b(x1)) -> x1 11.93/4.03 11.93/4.03 Q is empty. 11.93/4.03 We have to consider all minimal (P,Q,R)-chains. 11.93/4.03 ---------------------------------------- 11.93/4.03 11.93/4.03 (3) DependencyGraphProof (EQUIVALENT) 11.93/4.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 11.93/4.03 ---------------------------------------- 11.93/4.03 11.93/4.03 (4) 11.93/4.03 Obligation: 11.93/4.03 Q DP problem: 11.93/4.03 The TRS P consists of the following rules: 11.93/4.03 11.93/4.03 A(c(b(x1))) -> A(c(x1)) 11.93/4.03 A(c(b(x1))) -> A(a(c(x1))) 11.93/4.03 11.93/4.03 The TRS R consists of the following rules: 11.93/4.03 11.93/4.03 a(x1) -> b(c(x1)) 11.93/4.03 a(c(b(x1))) -> b(a(a(c(x1)))) 11.93/4.03 b(b(x1)) -> x1 11.93/4.03 11.93/4.03 Q is empty. 11.93/4.03 We have to consider all minimal (P,Q,R)-chains. 11.93/4.03 ---------------------------------------- 11.93/4.03 11.93/4.03 (5) QDPOrderProof (EQUIVALENT) 11.93/4.03 We use the reduction pair processor [LPAR04,JAR06]. 11.93/4.03 11.93/4.03 11.93/4.03 The following pairs can be oriented strictly and are deleted. 11.93/4.03 11.93/4.03 A(c(b(x1))) -> A(c(x1)) 11.93/4.03 A(c(b(x1))) -> A(a(c(x1))) 11.93/4.03 The remaining pairs can at least be oriented weakly. 11.93/4.03 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 11.93/4.03 11.93/4.03 <<< 11.93/4.03 POL(A(x_1)) = [[0A]] + [[0A, 0A, 0A]] * x_1 11.93/4.03 >>> 11.93/4.03 11.93/4.03 <<< 11.93/4.03 POL(c(x_1)) = [[0A], [0A], [-I]] + [[0A, -I, 0A], [0A, -I, 1A], [-I, -I, -I]] * x_1 11.93/4.03 >>> 11.93/4.03 11.93/4.03 <<< 11.93/4.03 POL(b(x_1)) = [[0A], [0A], [0A]] + [[-I, 0A, 0A], [0A, -I, 0A], [0A, -I, 1A]] * x_1
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to SRS_Standard 2019-03-29 03.29