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TRS_Innermost 2019-03-28 22.12 pair #432270746
details
property
value
status
complete
benchmark
test77.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
Mixed_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.09196 seconds
cpu usage
4.3873
user time
4.19793
system time
0.189373
max virtual memory
1.83454E7
max residence set size
306200.0
stage attributes
key
value
starexec-result
YES
output
4.32/2.06 YES 4.36/2.06 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 4.36/2.06 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.36/2.06 4.36/2.06 4.36/2.06 Termination w.r.t. Q of the given QTRS could be proven: 4.36/2.06 4.36/2.06 (0) QTRS 4.36/2.06 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 4.36/2.06 (2) QDP 4.36/2.06 (3) DependencyGraphProof [EQUIVALENT, 0 ms] 4.36/2.06 (4) AND 4.36/2.06 (5) QDP 4.36/2.06 (6) UsableRulesProof [EQUIVALENT, 0 ms] 4.36/2.06 (7) QDP 4.36/2.06 (8) QReductionProof [EQUIVALENT, 0 ms] 4.36/2.06 (9) QDP 4.36/2.06 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 4.36/2.06 (11) YES 4.36/2.06 (12) QDP 4.36/2.06 (13) UsableRulesProof [EQUIVALENT, 0 ms] 4.36/2.06 (14) QDP 4.36/2.06 (15) QReductionProof [EQUIVALENT, 0 ms] 4.36/2.06 (16) QDP 4.36/2.06 (17) TransformationProof [EQUIVALENT, 0 ms] 4.36/2.06 (18) QDP 4.36/2.06 (19) UsableRulesProof [EQUIVALENT, 0 ms] 4.36/2.06 (20) QDP 4.36/2.06 (21) QReductionProof [EQUIVALENT, 0 ms] 4.36/2.06 (22) QDP 4.36/2.06 (23) TransformationProof [EQUIVALENT, 0 ms] 4.36/2.06 (24) QDP 4.36/2.06 (25) DependencyGraphProof [EQUIVALENT, 0 ms] 4.36/2.06 (26) TRUE 4.36/2.06 4.36/2.06 4.36/2.06 ---------------------------------------- 4.36/2.06 4.36/2.06 (0) 4.36/2.06 Obligation: 4.36/2.06 Q restricted rewrite system: 4.36/2.06 The TRS R consists of the following rules: 4.36/2.06 4.36/2.06 +(X, 0) -> X 4.36/2.06 +(X, s(Y)) -> s(+(X, Y)) 4.36/2.06 double(X) -> +(X, X) 4.36/2.06 f(0, s(0), X) -> f(X, double(X), X) 4.36/2.06 g(X, Y) -> X 4.36/2.06 g(X, Y) -> Y 4.36/2.06 4.36/2.06 The set Q consists of the following terms: 4.36/2.06 4.36/2.06 +(x0, 0) 4.36/2.06 +(x0, s(x1)) 4.36/2.06 double(x0) 4.36/2.06 f(0, s(0), x0) 4.36/2.06 g(x0, x1) 4.36/2.06 4.36/2.06 4.36/2.06 ---------------------------------------- 4.36/2.06 4.36/2.06 (1) DependencyPairsProof (EQUIVALENT) 4.36/2.06 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 4.36/2.06 ---------------------------------------- 4.36/2.06 4.36/2.06 (2) 4.36/2.06 Obligation: 4.36/2.06 Q DP problem: 4.36/2.06 The TRS P consists of the following rules: 4.36/2.06 4.36/2.06 +^1(X, s(Y)) -> +^1(X, Y) 4.36/2.06 DOUBLE(X) -> +^1(X, X) 4.36/2.06 F(0, s(0), X) -> F(X, double(X), X) 4.36/2.06 F(0, s(0), X) -> DOUBLE(X) 4.36/2.06 4.36/2.06 The TRS R consists of the following rules: 4.36/2.06 4.36/2.06 +(X, 0) -> X 4.36/2.06 +(X, s(Y)) -> s(+(X, Y)) 4.36/2.06 double(X) -> +(X, X) 4.36/2.06 f(0, s(0), X) -> f(X, double(X), X) 4.36/2.06 g(X, Y) -> X 4.36/2.06 g(X, Y) -> Y 4.36/2.06 4.36/2.06 The set Q consists of the following terms: 4.36/2.06 4.36/2.06 +(x0, 0) 4.36/2.06 +(x0, s(x1)) 4.36/2.06 double(x0) 4.36/2.06 f(0, s(0), x0) 4.36/2.06 g(x0, x1) 4.36/2.06 4.36/2.06 We have to consider all minimal (P,Q,R)-chains. 4.36/2.06 ---------------------------------------- 4.36/2.06 4.36/2.06 (3) DependencyGraphProof (EQUIVALENT) 4.36/2.06 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes. 4.36/2.06 ---------------------------------------- 4.36/2.06 4.36/2.06 (4)
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