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TRS Standard pair #487067934
details
property
value
status
complete
benchmark
2.16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0207909 seconds
cpu usage
0.021183
user time
0.005102
system time
0.016081
max virtual memory
113188.0
max residence set size
5324.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) f(0) -> 1 f(s(x:S)) -> g(x:S,s(x:S)) g(0,y:S) -> y:S g(s(x:S),y:S) -> g(x:S,+(y:S,s(x:S))) g(s(x:S),y:S) -> g(x:S,s(+(y:S,x:S))) ) Problem 1: Dependency Pairs Processor: -> Pairs: +#(x:S,s(y:S)) -> +#(x:S,y:S) F(s(x:S)) -> G(x:S,s(x:S)) G(s(x:S),y:S) -> +#(y:S,s(x:S)) G(s(x:S),y:S) -> +#(y:S,x:S) G(s(x:S),y:S) -> G(x:S,+(y:S,s(x:S))) G(s(x:S),y:S) -> G(x:S,s(+(y:S,x:S))) -> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) f(0) -> 1 f(s(x:S)) -> g(x:S,s(x:S)) g(0,y:S) -> y:S g(s(x:S),y:S) -> g(x:S,+(y:S,s(x:S))) g(s(x:S),y:S) -> g(x:S,s(+(y:S,x:S))) Problem 1: SCC Processor: -> Pairs: +#(x:S,s(y:S)) -> +#(x:S,y:S) F(s(x:S)) -> G(x:S,s(x:S)) G(s(x:S),y:S) -> +#(y:S,s(x:S)) G(s(x:S),y:S) -> +#(y:S,x:S) G(s(x:S),y:S) -> G(x:S,+(y:S,s(x:S))) G(s(x:S),y:S) -> G(x:S,s(+(y:S,x:S))) -> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) f(0) -> 1 f(s(x:S)) -> g(x:S,s(x:S)) g(0,y:S) -> y:S g(s(x:S),y:S) -> g(x:S,+(y:S,s(x:S))) g(s(x:S),y:S) -> g(x:S,s(+(y:S,x:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: +#(x:S,s(y:S)) -> +#(x:S,y:S) ->->-> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) f(0) -> 1 f(s(x:S)) -> g(x:S,s(x:S)) g(0,y:S) -> y:S g(s(x:S),y:S) -> g(x:S,+(y:S,s(x:S))) g(s(x:S),y:S) -> g(x:S,s(+(y:S,x:S))) ->->Cycle: ->->-> Pairs: G(s(x:S),y:S) -> G(x:S,+(y:S,s(x:S))) G(s(x:S),y:S) -> G(x:S,s(+(y:S,x:S))) ->->-> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) f(0) -> 1 f(s(x:S)) -> g(x:S,s(x:S)) g(0,y:S) -> y:S g(s(x:S),y:S) -> g(x:S,+(y:S,s(x:S))) g(s(x:S),y:S) -> g(x:S,s(+(y:S,x:S))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: +#(x:S,s(y:S)) -> +#(x:S,y:S) -> Rules: +(x:S,0) -> x:S +(x:S,s(y:S)) -> s(+(x:S,y:S)) f(0) -> 1 f(s(x:S)) -> g(x:S,s(x:S)) g(0,y:S) -> y:S g(s(x:S),y:S) -> g(x:S,+(y:S,s(x:S))) g(s(x:S),y:S) -> g(x:S,s(+(y:S,x:S))) ->Projection: pi(+#) = 2 Problem 1.1: SCC Processor: -> Pairs:
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