details

property	value
status	complete
benchmark	Ex49_GM04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0535531 seconds
cpu usage	0.041194
user time	0.020259
system time	0.020935
max virtual memory	113188.0
max residence set size	5684.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S X:S Y:S) (RULES div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0) geq(0,s(Y:S)) -> ffalse geq(s(X:S),s(Y:S)) -> geq(X:S,Y:S) geq(X:S,0) -> ttrue if(ffalse,X:S,Y:S) -> Y:S if(ttrue,X:S,Y:S) -> X:S minus(0,Y:S) -> 0 minus(s(X:S),s(Y:S)) -> minus(X:S,Y:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0) geq(0,s(Y:S)) -> ffalse geq(s(X:S),s(Y:S)) -> geq(X:S,Y:S) geq(X:S,0) -> ttrue if(ffalse,X:S,Y:S) -> Y:S if(ttrue,X:S,Y:S) -> X:S minus(0,Y:S) -> 0 minus(s(X:S),s(Y:S)) -> minus(X:S,Y:S) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: DIV(s(X:S),s(Y:S)) -> DIV(minus(X:S,Y:S),s(Y:S)) DIV(s(X:S),s(Y:S)) -> GEQ(X:S,Y:S) DIV(s(X:S),s(Y:S)) -> IF(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0) DIV(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) GEQ(s(X:S),s(Y:S)) -> GEQ(X:S,Y:S) MINUS(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) -> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0) geq(0,s(Y:S)) -> ffalse geq(s(X:S),s(Y:S)) -> geq(X:S,Y:S) geq(X:S,0) -> ttrue if(ffalse,X:S,Y:S) -> Y:S if(ttrue,X:S,Y:S) -> X:S minus(0,Y:S) -> 0 minus(s(X:S),s(Y:S)) -> minus(X:S,Y:S) Problem 1: SCC Processor: -> Pairs: DIV(s(X:S),s(Y:S)) -> DIV(minus(X:S,Y:S),s(Y:S)) DIV(s(X:S),s(Y:S)) -> GEQ(X:S,Y:S) DIV(s(X:S),s(Y:S)) -> IF(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0) DIV(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) GEQ(s(X:S),s(Y:S)) -> GEQ(X:S,Y:S) MINUS(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) -> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0) geq(0,s(Y:S)) -> ffalse geq(s(X:S),s(Y:S)) -> geq(X:S,Y:S) geq(X:S,0) -> ttrue if(ffalse,X:S,Y:S) -> Y:S if(ttrue,X:S,Y:S) -> X:S minus(0,Y:S) -> 0 minus(s(X:S),s(Y:S)) -> minus(X:S,Y:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MINUS(s(X:S),s(Y:S)) -> MINUS(X:S,Y:S) ->->-> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0) geq(0,s(Y:S)) -> ffalse geq(s(X:S),s(Y:S)) -> geq(X:S,Y:S) geq(X:S,0) -> ttrue if(ffalse,X:S,Y:S) -> Y:S if(ttrue,X:S,Y:S) -> X:S minus(0,Y:S) -> 0 minus(s(X:S),s(Y:S)) -> minus(X:S,Y:S) ->->Cycle: ->->-> Pairs: GEQ(s(X:S),s(Y:S)) -> GEQ(X:S,Y:S) ->->-> Rules: div(0,s(Y:S)) -> 0 div(s(X:S),s(Y:S)) -> if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0) geq(0,s(Y:S)) -> ffalse geq(s(X:S),s(Y:S)) -> geq(X:S,Y:S) geq(X:S,0) -> ttrue if(ffalse,X:S,Y:S) -> Y:S if(ttrue,X:S,Y:S) -> X:S minus(0,Y:S) -> 0 popout

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