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TRS Innermost pair #487092946
details
property
value
status
complete
benchmark
#4.27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0661071 seconds
cpu usage
0.053359
user time
0.020913
system time
0.032446
max virtual memory
113188.0
max residence set size
5376.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> if(le(x:S,s(y:S)),0,p(minus(x:S,p(s(y:S))))) p(0) -> 0 p(s(x:S)) -> x:S ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MINUS(x:S,s(y:S)) -> IF(le(x:S,s(y:S)),0,p(minus(x:S,p(s(y:S))))) MINUS(x:S,s(y:S)) -> LE(x:S,s(y:S)) MINUS(x:S,s(y:S)) -> MINUS(x:S,p(s(y:S))) MINUS(x:S,s(y:S)) -> P(minus(x:S,p(s(y:S)))) MINUS(x:S,s(y:S)) -> P(s(y:S)) -> Rules: if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> if(le(x:S,s(y:S)),0,p(minus(x:S,p(s(y:S))))) p(0) -> 0 p(s(x:S)) -> x:S Problem 1: SCC Processor: -> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MINUS(x:S,s(y:S)) -> IF(le(x:S,s(y:S)),0,p(minus(x:S,p(s(y:S))))) MINUS(x:S,s(y:S)) -> LE(x:S,s(y:S)) MINUS(x:S,s(y:S)) -> MINUS(x:S,p(s(y:S))) MINUS(x:S,s(y:S)) -> P(minus(x:S,p(s(y:S)))) MINUS(x:S,s(y:S)) -> P(s(y:S)) -> Rules: if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> if(le(x:S,s(y:S)),0,p(minus(x:S,p(s(y:S))))) p(0) -> 0 p(s(x:S)) -> x:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) ->->-> Rules: if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> if(le(x:S,s(y:S)),0,p(minus(x:S,p(s(y:S))))) p(0) -> 0 p(s(x:S)) -> x:S ->->Cycle: ->->-> Pairs: MINUS(x:S,s(y:S)) -> MINUS(x:S,p(s(y:S))) ->->-> Rules: if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(x:S,0) -> x:S minus(x:S,s(y:S)) -> if(le(x:S,s(y:S)),0,p(minus(x:S,p(s(y:S))))) p(0) -> 0 p(s(x:S)) -> x:S The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) -> Rules: if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse
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