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TRS_Equational 2019-03-21 05.09 pair #429997153
details
property
value
status
complete
benchmark
AC42.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n002.star.cs.uiowa.edu
space
Mixed_C
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.07522 seconds
cpu usage
4.21495
user time
4.0365
system time
0.178454
max virtual memory
1.8282884E7
max residence set size
249620.0
stage attributes
key
value
starexec-result
YES
output
4.01/2.05 YES 4.01/2.06 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 4.01/2.06 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.01/2.06 4.01/2.06 4.01/2.06 Termination of the given ETRS could be proven: 4.01/2.06 4.01/2.06 (0) ETRS 4.01/2.06 (1) EquationalDependencyPairsProof [EQUIVALENT, 14 ms] 4.01/2.06 (2) EDP 4.01/2.06 (3) EDependencyGraphProof [EQUIVALENT, 0 ms] 4.01/2.06 (4) AND 4.01/2.06 (5) EDP 4.01/2.06 (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] 4.01/2.06 (7) EDP 4.01/2.06 (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] 4.01/2.06 (9) EDP 4.01/2.06 (10) PisEmptyProof [EQUIVALENT, 0 ms] 4.01/2.06 (11) YES 4.01/2.06 (12) EDP 4.01/2.06 (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] 4.01/2.06 (14) EDP 4.01/2.06 (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] 4.01/2.06 (16) EDP 4.01/2.06 (17) PisEmptyProof [EQUIVALENT, 0 ms] 4.01/2.06 (18) YES 4.01/2.06 (19) EDP 4.01/2.06 (20) EDPPoloProof [EQUIVALENT, 0 ms] 4.01/2.06 (21) EDP 4.01/2.06 (22) PisEmptyProof [EQUIVALENT, 0 ms] 4.01/2.06 (23) YES 4.01/2.06 4.01/2.06 4.01/2.06 ---------------------------------------- 4.01/2.06 4.01/2.06 (0) 4.01/2.06 Obligation: 4.01/2.06 Equational rewrite system: 4.01/2.06 The TRS R consists of the following rules: 4.01/2.06 4.01/2.06 le(0, y) -> true 4.01/2.06 le(s(x), 0) -> false 4.01/2.06 le(s(x), s(y)) -> le(x, y) 4.01/2.06 pred(s(x)) -> x 4.01/2.06 minus(x, 0) -> x 4.01/2.06 minus(x, s(y)) -> pred(minus(x, y)) 4.01/2.06 gcd(0, y) -> y 4.01/2.06 gcd(s(x), 0) -> s(x) 4.01/2.06 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 4.01/2.06 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) 4.01/2.06 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) 4.01/2.06 4.01/2.06 The set E consists of the following equations: 4.01/2.06 4.01/2.06 gcd(x, y) == gcd(y, x) 4.01/2.06 4.01/2.06 4.01/2.06 ---------------------------------------- 4.01/2.06 4.01/2.06 (1) EquationalDependencyPairsProof (EQUIVALENT) 4.01/2.06 Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem: 4.01/2.06 The TRS P consists of the following rules: 4.01/2.06 4.01/2.06 LE(s(x), s(y)) -> LE(x, y) 4.01/2.06 MINUS(x, s(y)) -> PRED(minus(x, y)) 4.01/2.06 MINUS(x, s(y)) -> MINUS(x, y) 4.01/2.06 GCD(s(x), s(y)) -> IF_GCD(le(y, x), s(x), s(y)) 4.01/2.06 GCD(s(x), s(y)) -> LE(y, x) 4.01/2.06 IF_GCD(true, s(x), s(y)) -> GCD(minus(x, y), s(y)) 4.01/2.06 IF_GCD(true, s(x), s(y)) -> MINUS(x, y) 4.01/2.06 IF_GCD(false, s(x), s(y)) -> GCD(minus(y, x), s(x)) 4.01/2.06 IF_GCD(false, s(x), s(y)) -> MINUS(y, x) 4.01/2.06 4.01/2.06 The TRS R consists of the following rules: 4.01/2.06 4.01/2.06 le(0, y) -> true 4.01/2.06 le(s(x), 0) -> false 4.01/2.06 le(s(x), s(y)) -> le(x, y) 4.01/2.06 pred(s(x)) -> x 4.01/2.06 minus(x, 0) -> x 4.01/2.06 minus(x, s(y)) -> pred(minus(x, y)) 4.01/2.06 gcd(0, y) -> y 4.01/2.06 gcd(s(x), 0) -> s(x) 4.01/2.06 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 4.01/2.06 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) 4.01/2.06 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) 4.01/2.06 4.01/2.06 The set E consists of the following equations: 4.01/2.06 4.01/2.06 gcd(x, y) == gcd(y, x) 4.01/2.06 4.01/2.06 The set E# consists of the following equations: 4.01/2.06 4.01/2.06 GCD(x, y) == GCD(y, x) 4.01/2.06 4.01/2.06 We have to consider all minimal (P,E#,R,E)-chains 4.01/2.06 4.01/2.06 ---------------------------------------- 4.01/2.06 4.01/2.06 (2)
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