/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^2)) * Step 1: Sum. WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () *** Step 1.a:1.a:1: Ara. MAYBE + Considered Problem: - Strict TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true} + Applied Processor: Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "0") :: [] -(0)-> "A"(0, 0, 0) F (TrsFun "1") :: [] -(0)-> "A"(0, 0, 0) F (TrsFun "c") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0) F (TrsFun "f") :: ["A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "false") :: [] -(0)-> "A"(0, 0, 1) F (TrsFun "false") :: [] -(0)-> "A"(0, 0, 0) F (TrsFun "g") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "if") :: ["A"(0, 0, 1) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "main") :: ["A"(0, 0, 1) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "s") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0) F (TrsFun "true") :: [] -(0)-> "A"(0, 0, 1) F (TrsFun "true") :: [] -(0)-> "A"(0, 0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) main(x1,x2,x3) -> if(x1,x2,x3) 2. Weak: *** Step 1.a:1.b:1: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x){x -> s(x)} = f(s(x)) ->^+ f(x) = C[f(x) = f(x){}] ** Step 1.b:1: DependencyPairs. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs f#(0()) -> c_1() f#(1()) -> c_2() f#(s(x)) -> c_3(f#(x)) g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)) if#(false(),s(x),s(y)) -> c_6() if#(true(),s(x),s(y)) -> c_7() Weak DPs and mark the set of starting terms. ** Step 1.b:2: PredecessorEstimation. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: f#(0()) -> c_1() f#(1()) -> c_2() f#(s(x)) -> c_3(f#(x)) g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)) if#(false(),s(x),s(y)) -> c_6() if#(true(),s(x),s(y)) -> c_7() - Weak TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/4,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1,2,6,7} by application of Pre({1,2,6,7}) = {3,5}. Here rules are labelled as follows: 1: f#(0()) -> c_1() 2: f#(1()) -> c_2() 3: f#(s(x)) -> c_3(f#(x)) 4: g#(x,c(y)) -> c_4(g#(x,y)) 5: g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)) 6: if#(false(),s(x),s(y)) -> c_6() 7: if#(true(),s(x),s(y)) -> c_7() ** Step 1.b:3: RemoveWeakSuffixes. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: f#(s(x)) -> c_3(f#(x)) g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)) - Weak DPs: f#(0()) -> c_1() f#(1()) -> c_2() if#(false(),s(x),s(y)) -> c_6() if#(true(),s(x),s(y)) -> c_7() - Weak TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/4,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:S:f#(s(x)) -> c_3(f#(x)) -->_1 f#(1()) -> c_2():5 -->_1 f#(0()) -> c_1():4 -->_1 f#(s(x)) -> c_3(f#(x)):1 2:S:g#(x,c(y)) -> c_4(g#(x,y)) -->_1 g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)):3 -->_1 g#(x,c(y)) -> c_4(g#(x,y)):2 3:S:g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)) -->_3 f#(1()) -> c_2():5 -->_3 f#(0()) -> c_1():4 -->_4 g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)):3 -->_4 g#(x,c(y)) -> c_4(g#(x,y)):2 -->_3 f#(s(x)) -> c_3(f#(x)):1 4:W:f#(0()) -> c_1() 5:W:f#(1()) -> c_2() 6:W:if#(false(),s(x),s(y)) -> c_6() 7:W:if#(true(),s(x),s(y)) -> c_7() The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 7: if#(true(),s(x),s(y)) -> c_7() 6: if#(false(),s(x),s(y)) -> c_6() 4: f#(0()) -> c_1() 5: f#(1()) -> c_2() ** Step 1.b:4: SimplifyRHS. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: f#(s(x)) -> c_3(f#(x)) g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)) - Weak TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/4,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: SimplifyRHS + Details: Consider the dependency graph 1:S:f#(s(x)) -> c_3(f#(x)) -->_1 f#(s(x)) -> c_3(f#(x)):1 2:S:g#(x,c(y)) -> c_4(g#(x,y)) -->_1 g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)):3 -->_1 g#(x,c(y)) -> c_4(g#(x,y)):2 3:S:g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)) -->_4 g#(x,c(y)) -> c_5(g#(x,if(f(x),c(g(s(x),y)),c(y))),if#(f(x),c(g(s(x),y)),c(y)),f#(x),g#(s(x),y)):3 -->_4 g#(x,c(y)) -> c_4(g#(x,y)):2 -->_3 f#(s(x)) -> c_3(f#(x)):1 Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified: g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)) ** Step 1.b:5: UsableRules. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: f#(s(x)) -> c_3(f#(x)) g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)) - Weak TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> c(g(x,y)) g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y))) if(false(),s(x),s(y)) -> s(y) if(true(),s(x),s(y)) -> s(x) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: f#(s(x)) -> c_3(f#(x)) g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)) ** Step 1.b:6: DecomposeDG. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: f#(s(x)) -> c_3(f#(x)) g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: DecomposeDG {onSelection = all below first cut in WDG, onUpper = Nothing, onLower = Nothing} + Details: We decompose the input problem according to the dependency graph into the upper component g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)) and a lower component f#(s(x)) -> c_3(f#(x)) Further, following extension rules are added to the lower component. g#(x,c(y)) -> f#(x) g#(x,c(y)) -> g#(x,y) g#(x,c(y)) -> g#(s(x),y) *** Step 1.b:6.a:1: SimplifyRHS. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: SimplifyRHS + Details: Consider the dependency graph 1:S:g#(x,c(y)) -> c_4(g#(x,y)) -->_1 g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)):2 -->_1 g#(x,c(y)) -> c_4(g#(x,y)):1 2:S:g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)) -->_2 g#(x,c(y)) -> c_5(f#(x),g#(s(x),y)):2 -->_2 g#(x,c(y)) -> c_4(g#(x,y)):1 Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified: g#(x,c(y)) -> c_5(g#(s(x),y)) *** Step 1.b:6.a:2: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(g#(s(x),y)) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(c_4) = {1}, uargs(c_5) = {1} Following symbols are considered usable: {f#,g#,if#} TcT has computed the following interpretation: p(0) = [0] p(1) = [2] p(c) = [1] x1 + [4] p(f) = [1] x1 + [2] p(false) = [0] p(g) = [0] p(if) = [2] x1 + [4] x3 + [2] p(s) = [0] p(true) = [0] p(f#) = [1] x1 + [1] p(g#) = [3] x1 + [1] x2 + [0] p(if#) = [1] x1 + [1] x2 + [8] x3 + [1] p(c_1) = [1] p(c_2) = [2] p(c_3) = [8] p(c_4) = [1] x1 + [3] p(c_5) = [1] x1 + [4] p(c_6) = [1] p(c_7) = [1] Following rules are strictly oriented: g#(x,c(y)) = [3] x + [1] y + [4] > [3] x + [1] y + [3] = c_4(g#(x,y)) Following rules are (at-least) weakly oriented: g#(x,c(y)) = [3] x + [1] y + [4] >= [1] y + [4] = c_5(g#(s(x),y)) *** Step 1.b:6.a:3: WeightGap. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: g#(x,c(y)) -> c_5(g#(s(x),y)) - Weak DPs: g#(x,c(y)) -> c_4(g#(x,y)) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following constant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(c_4) = {1}, uargs(c_5) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [0] p(1) = [0] p(c) = [1] x1 + [3] p(f) = [0] p(false) = [0] p(g) = [0] p(if) = [0] p(s) = [1] x1 + [1] p(true) = [0] p(f#) = [0] p(g#) = [4] x1 + [4] x2 + [13] p(if#) = [0] p(c_1) = [0] p(c_2) = [0] p(c_3) = [8] x1 + [0] p(c_4) = [1] x1 + [0] p(c_5) = [1] x1 + [0] p(c_6) = [0] p(c_7) = [0] Following rules are strictly oriented: g#(x,c(y)) = [4] x + [4] y + [25] > [4] x + [4] y + [17] = c_5(g#(s(x),y)) Following rules are (at-least) weakly oriented: g#(x,c(y)) = [4] x + [4] y + [25] >= [4] x + [4] y + [13] = c_4(g#(x,y)) Further, it can be verified that all rules not oriented are covered by the weightgap condition. *** Step 1.b:6.a:4: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak DPs: g#(x,c(y)) -> c_4(g#(x,y)) g#(x,c(y)) -> c_5(g#(s(x),y)) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). *** Step 1.b:6.b:1: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(s(x)) -> c_3(f#(x)) - Weak DPs: g#(x,c(y)) -> f#(x) g#(x,c(y)) -> g#(x,y) g#(x,c(y)) -> g#(s(x),y) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(c_3) = {1} Following symbols are considered usable: {f#,g#,if#} TcT has computed the following interpretation: p(0) = [1] p(1) = [0] p(c) = [1] x1 + [4] p(f) = [1] x1 + [8] p(false) = [1] p(g) = [2] x2 + [1] p(if) = [1] x3 + [1] p(s) = [1] x1 + [8] p(true) = [0] p(f#) = [2] x1 + [1] p(g#) = [2] x1 + [4] x2 + [4] p(if#) = [1] x2 + [1] p(c_1) = [0] p(c_2) = [2] p(c_3) = [1] x1 + [7] p(c_4) = [1] x1 + [0] p(c_5) = [2] x1 + [0] p(c_6) = [1] p(c_7) = [1] Following rules are strictly oriented: f#(s(x)) = [2] x + [17] > [2] x + [8] = c_3(f#(x)) Following rules are (at-least) weakly oriented: g#(x,c(y)) = [2] x + [4] y + [20] >= [2] x + [1] = f#(x) g#(x,c(y)) = [2] x + [4] y + [20] >= [2] x + [4] y + [4] = g#(x,y) g#(x,c(y)) = [2] x + [4] y + [20] >= [2] x + [4] y + [20] = g#(s(x),y) *** Step 1.b:6.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak DPs: f#(s(x)) -> c_3(f#(x)) g#(x,c(y)) -> f#(x) g#(x,c(y)) -> g#(x,y) g#(x,c(y)) -> g#(s(x),y) - Signature: {f/1,g/2,if/3,f#/1,g#/2,if#/3} / {0/0,1/0,c/1,false/0,s/1,true/0,c_1/0,c_2/0,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0} - Obligation: innermost runtime complexity wrt. defined symbols {f#,g#,if#} and constructors {0,1,c,false,s,true} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^2))