details

property	value
status	complete
benchmark	t002.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	20.2467 seconds
cpu usage	20.1869
user time	18.5134
system time	1.67352
max virtual memory	598944.0
max residence set size	6232.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S leq(0,y:S) -> ttrue leq(s(x:S),0) -> ffalse leq(s(x:S),s(y:S)) -> leq(x:S,y:S) mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if(leq(y:S,x:S),mod(-(s(x:S),s(y:S)),s(y:S)),s(x:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S leq(0,y:S) -> ttrue leq(s(x:S),0) -> ffalse leq(s(x:S),s(y:S)) -> leq(x:S,y:S) mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if(leq(y:S,x:S),mod(-(s(x:S),s(y:S)),s(y:S)),s(x:S)) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) LEQ(s(x:S),s(y:S)) -> LEQ(x:S,y:S) MOD(s(x:S),s(y:S)) -> -#(s(x:S),s(y:S)) MOD(s(x:S),s(y:S)) -> IF(leq(y:S,x:S),mod(-(s(x:S),s(y:S)),s(y:S)),s(x:S)) MOD(s(x:S),s(y:S)) -> LEQ(y:S,x:S) MOD(s(x:S),s(y:S)) -> MOD(-(s(x:S),s(y:S)),s(y:S)) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S leq(0,y:S) -> ttrue leq(s(x:S),0) -> ffalse leq(s(x:S),s(y:S)) -> leq(x:S,y:S) mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if(leq(y:S,x:S),mod(-(s(x:S),s(y:S)),s(y:S)),s(x:S)) Problem 1: SCC Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) LEQ(s(x:S),s(y:S)) -> LEQ(x:S,y:S) MOD(s(x:S),s(y:S)) -> -#(s(x:S),s(y:S)) MOD(s(x:S),s(y:S)) -> IF(leq(y:S,x:S),mod(-(s(x:S),s(y:S)),s(y:S)),s(x:S)) MOD(s(x:S),s(y:S)) -> LEQ(y:S,x:S) MOD(s(x:S),s(y:S)) -> MOD(-(s(x:S),s(y:S)),s(y:S)) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S leq(0,y:S) -> ttrue leq(s(x:S),0) -> ffalse leq(s(x:S),s(y:S)) -> leq(x:S,y:S) mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if(leq(y:S,x:S),mod(-(s(x:S),s(y:S)),s(y:S)),s(x:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: LEQ(s(x:S),s(y:S)) -> LEQ(x:S,y:S) ->->-> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S leq(0,y:S) -> ttrue leq(s(x:S),0) -> ffalse leq(s(x:S),s(y:S)) -> leq(x:S,y:S) mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if(leq(y:S,x:S),mod(-(s(x:S),s(y:S)),s(y:S)),s(x:S)) ->->Cycle: ->->-> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) ->->-> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S if(ffalse,x:S,y:S) -> y:S popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard