YES Problem 1: (VAR v_NonEmpty:S x1:S) (RULES #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ) Problem 1: Dependency Pairs Processor: -> Pairs: ##(#(0(0(x1:S)))) -> ##(#(x1:S)) ##(#(0(0(x1:S)))) -> ##(x1:S) ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: SCC Processor: -> Pairs: ##(#(0(0(x1:S)))) -> ##(#(x1:S)) ##(#(0(0(x1:S)))) -> ##(x1:S) ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ##(#(0(0(x1:S)))) -> ##(#(x1:S)) ##(#(0(0(x1:S)))) -> ##(x1:S) ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: ##(#(0(0(x1:S)))) -> ##(#(x1:S)) ##(#(0(0(x1:S)))) -> ##(x1:S) ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 2 [0](X) = 2.X + 2 [1](X) = 2.X + 2 [$](X) = 2.X + 2 [*](X) = 2.X + 2 [##](X) = 2.X + 2 [0#](X) = X + 2 [1#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: ##(#(0(0(x1:S)))) -> ##(x1:S) ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ##(#(0(0(x1:S)))) -> ##(x1:S) ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: ##(#(0(0(x1:S)))) -> ##(x1:S) ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 1 [0](X) = 2.X + 1 [1](X) = 2.X + 1 [$](X) = 1 [*](X) = 2.X + 1 [##](X) = 2.X + 1 [0#](X) = X + 2 [1#](X) = 2.X Problem 1: SCC Processor: -> Pairs: ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S))) ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = X [0](X) = X + 1 [1](X) = X + 1 [$](X) = 2.X + 2 [*](X) = X [##](X) = X + 1 [0#](X) = X + 2 [1#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S)))) ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 2 [0](X) = 2.X + 2 [1](X) = 2.X + 2 [$](X) = 2.X + 1 [*](X) = 2.X + 2 [##](X) = 2.X + 2 [0#](X) = X + 2 [1#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: ##(#(1(1(x1:S)))) -> ##(#(x1:S)) ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 2 [0](X) = 2.X + 2 [1](X) = 2.X + 2 [$](X) = 2.X + 2 [*](X) = 2.X + 2 [##](X) = 2.X + 2 [0#](X) = 2.X + 1 [1#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: ##(#(1(1(x1:S)))) -> ##(x1:S) ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 2 [0](X) = 2.X + 2 [1](X) = 2.X + 2 [$](X) = X + 2 [*](X) = 2.X + 2 [##](X) = 2.X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S))) ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 2 [0](X) = 2.X + 2 [1](X) = 2.X + 2 [$](X) = 2.X + 2 [*](X) = 2.X + 2 [##](X) = 2.X [0#](X) = 2.X [1#](X) = 2.X Problem 1: SCC Processor: -> Pairs: ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S)))) 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 2 [0](X) = 2.X + 2 [1](X) = 2.X + 2 [$](X) = 2.X + 2 [*](X) = 2.X + 2 [##](X) = 2.X + 2 [0#](X) = X + 2 [1#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> ##(#(x1:S)) 1#(1(*(*(x1:S)))) -> ##(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(*(*(x1:S)))) -> 1#(1(x1:S)) 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 2 [0](X) = 2.X + 2 [1](X) = 2.X + 2 [$](X) = X + 1 [*](X) = 2.X + 2 [0#](X) = 2.X + 1 [1#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) ->->-> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(*(*(x1:S)))) -> 1#(x1:S) 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) -> Usable rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [#](X) = 2.X + 2 [0](X) = X [1](X) = X [$](X) = 2.X [*](X) = 2.X + 2 [0#](X) = X + 1 [1#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S))) 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S)))) -> Rules: #(#(#(#(x1:S)))) -> #(#(x1:S)) #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S)))) #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S)))) #(#($($(x1:S)))) -> *(*($($(x1:S)))) #(#(*(*(x1:S)))) -> *(*(x1:S)) 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S)))) 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S)))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.