details

property	value
status	complete
benchmark	AC44.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n176.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.13665 seconds
cpu usage	4.69138
user time	4.50235
system time	0.189035
max virtual memory	1.8277816E7
max residence set size	260336.0

stage attributes

key	value
starexec-result	YES

output

4.32/2.09 YES 4.63/2.10 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 4.63/2.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.63/2.10 4.63/2.10 4.63/2.10 Termination of the given ETRS could be proven: 4.63/2.10 4.63/2.10 (0) ETRS 4.63/2.10 (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] 4.63/2.10 (2) EDP 4.63/2.10 (3) EDependencyGraphProof [EQUIVALENT, 0 ms] 4.63/2.10 (4) AND 4.63/2.10 (5) EDP 4.63/2.10 (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] 4.63/2.10 (7) EDP 4.63/2.10 (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] 4.63/2.10 (9) EDP 4.63/2.10 (10) PisEmptyProof [EQUIVALENT, 0 ms] 4.63/2.10 (11) YES 4.63/2.10 (12) EDP 4.63/2.10 (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] 4.63/2.10 (14) EDP 4.63/2.10 (15) EDPPoloProof [EQUIVALENT, 0 ms] 4.63/2.10 (16) EDP 4.63/2.10 (17) PisEmptyProof [EQUIVALENT, 0 ms] 4.63/2.10 (18) YES 4.63/2.10 (19) EDP 4.63/2.10 (20) EDPPoloProof [EQUIVALENT, 27 ms] 4.63/2.10 (21) EDP 4.63/2.10 (22) EDependencyGraphProof [EQUIVALENT, 0 ms] 4.63/2.10 (23) TRUE 4.63/2.10 4.63/2.10 4.63/2.10 ---------------------------------------- 4.63/2.10 4.63/2.10 (0) 4.63/2.10 Obligation: 4.63/2.10 Equational rewrite system: 4.63/2.10 The TRS R consists of the following rules: 4.63/2.10 4.63/2.10 le(0, y) -> true 4.63/2.10 le(s(x), 0) -> false 4.63/2.10 le(s(x), s(y)) -> le(x, y) 4.63/2.10 minus(0, y) -> 0 4.63/2.10 minus(s(x), y) -> if_minus(le(s(x), y), s(x), y) 4.63/2.10 if_minus(true, s(x), y) -> 0 4.63/2.10 if_minus(false, s(x), y) -> s(minus(x, y)) 4.63/2.10 gcd(0, y) -> y 4.63/2.10 gcd(s(x), 0) -> s(x) 4.63/2.10 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 4.63/2.10 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) 4.63/2.10 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) 4.63/2.10 4.63/2.10 The set E consists of the following equations: 4.63/2.10 4.63/2.10 gcd(x, y) == gcd(y, x) 4.63/2.10 4.63/2.10 4.63/2.10 ---------------------------------------- 4.63/2.10 4.63/2.10 (1) EquationalDependencyPairsProof (EQUIVALENT) 4.63/2.10 Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem: 4.63/2.10 The TRS P consists of the following rules: 4.63/2.10 4.63/2.10 LE(s(x), s(y)) -> LE(x, y) 4.63/2.10 MINUS(s(x), y) -> IF_MINUS(le(s(x), y), s(x), y) 4.63/2.10 MINUS(s(x), y) -> LE(s(x), y) 4.63/2.10 IF_MINUS(false, s(x), y) -> MINUS(x, y) 4.63/2.10 GCD(s(x), s(y)) -> IF_GCD(le(y, x), s(x), s(y)) 4.63/2.10 GCD(s(x), s(y)) -> LE(y, x) 4.63/2.10 IF_GCD(true, s(x), s(y)) -> GCD(minus(x, y), s(y)) 4.63/2.10 IF_GCD(true, s(x), s(y)) -> MINUS(x, y) 4.63/2.10 IF_GCD(false, s(x), s(y)) -> GCD(minus(y, x), s(x)) 4.63/2.10 IF_GCD(false, s(x), s(y)) -> MINUS(y, x) 4.63/2.10 4.63/2.10 The TRS R consists of the following rules: 4.63/2.10 4.63/2.10 le(0, y) -> true 4.63/2.10 le(s(x), 0) -> false 4.63/2.10 le(s(x), s(y)) -> le(x, y) 4.63/2.10 minus(0, y) -> 0 4.63/2.10 minus(s(x), y) -> if_minus(le(s(x), y), s(x), y) 4.63/2.10 if_minus(true, s(x), y) -> 0 4.63/2.10 if_minus(false, s(x), y) -> s(minus(x, y)) 4.63/2.10 gcd(0, y) -> y 4.63/2.10 gcd(s(x), 0) -> s(x) 4.63/2.10 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 4.63/2.10 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) 4.63/2.10 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) 4.63/2.10 4.63/2.10 The set E consists of the following equations: 4.63/2.10 4.63/2.10 gcd(x, y) == gcd(y, x) 4.63/2.10 4.63/2.10 The set E# consists of the following equations: 4.63/2.10 4.63/2.10 GCD(x, y) == GCD(y, x) 4.63/2.10 4.63/2.10 We have to consider all minimal (P,E#,R,E)-chains 4.63/2.10 popout

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all output return to TRS_Equational 2019-03-21 05.09