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TRS Equational pair #487092861
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
n150.star.cs.uiowa.edu
space
Mixed_C
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.590488 seconds
cpu usage
0.589691
user time
0.3232
system time
0.266491
max virtual memory
686808.0
max residence set size
5160.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR x y) (THEORY (C gcd)) (RULES gcd(0,y) -> y gcd(s(x),0) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false,s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true,s(x),s(y)) -> gcd(minus(x,y),s(y)) if_minus(false,s(x),y) -> s(minus(x,y)) if_minus(true,s(x),y) -> 0 le(0,y) -> true le(s(x),0) -> false le(s(x),s(y)) -> le(x,y) minus(0,y) -> 0 minus(s(x),y) -> if_minus(le(s(x),y),s(x),y) ) Problem 1: Dependency Pairs Processor: -> FAxioms: GCD(x2,x3) = GCD(x3,x2) -> Pairs: GCD(s(x),s(y)) -> IF_GCD(le(y,x),s(x),s(y)) GCD(s(x),s(y)) -> LE(y,x) IF_GCD(false,s(x),s(y)) -> GCD(minus(y,x),s(x)) IF_GCD(false,s(x),s(y)) -> MINUS(y,x) IF_GCD(true,s(x),s(y)) -> GCD(minus(x,y),s(y)) IF_GCD(true,s(x),s(y)) -> MINUS(x,y) IF_MINUS(false,s(x),y) -> MINUS(x,y) LE(s(x),s(y)) -> LE(x,y) MINUS(s(x),y) -> IF_MINUS(le(s(x),y),s(x),y) MINUS(s(x),y) -> LE(s(x),y) -> EAxioms: gcd(x2,x3) = gcd(x3,x2) -> Rules: gcd(0,y) -> y gcd(s(x),0) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false,s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true,s(x),s(y)) -> gcd(minus(x,y),s(y)) if_minus(false,s(x),y) -> s(minus(x,y)) if_minus(true,s(x),y) -> 0 le(0,y) -> true le(s(x),0) -> false le(s(x),s(y)) -> le(x,y) minus(0,y) -> 0 minus(s(x),y) -> if_minus(le(s(x),y),s(x),y) -> SRules: Empty Problem 1: SCC Processor: -> FAxioms: GCD(x2,x3) = GCD(x3,x2) -> Pairs: GCD(s(x),s(y)) -> IF_GCD(le(y,x),s(x),s(y)) GCD(s(x),s(y)) -> LE(y,x) IF_GCD(false,s(x),s(y)) -> GCD(minus(y,x),s(x)) IF_GCD(false,s(x),s(y)) -> MINUS(y,x) IF_GCD(true,s(x),s(y)) -> GCD(minus(x,y),s(y)) IF_GCD(true,s(x),s(y)) -> MINUS(x,y) IF_MINUS(false,s(x),y) -> MINUS(x,y) LE(s(x),s(y)) -> LE(x,y) MINUS(s(x),y) -> IF_MINUS(le(s(x),y),s(x),y) MINUS(s(x),y) -> LE(s(x),y) -> EAxioms: gcd(x2,x3) = gcd(x3,x2) -> Rules: gcd(0,y) -> y gcd(s(x),0) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false,s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true,s(x),s(y)) -> gcd(minus(x,y),s(y)) if_minus(false,s(x),y) -> s(minus(x,y)) if_minus(true,s(x),y) -> 0 le(0,y) -> true le(s(x),0) -> false le(s(x),s(y)) -> le(x,y) minus(0,y) -> 0 minus(s(x),y) -> if_minus(le(s(x),y),s(x),y) -> SRules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: LE(s(x),s(y)) -> LE(x,y) -> FAxioms: gcd(x2,x3) -> gcd(x3,x2) -> EAxioms: gcd(x2,x3) = gcd(x3,x2) ->->-> Rules: gcd(0,y) -> y gcd(s(x),0) -> s(x)
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