0.00/0.15 YES 0.00/0.16 Input TRS: 0.00/0.16 AC symbols: plus app 0.00/0.16 1: if(true(),x,y) -> x 0.00/0.16 2: if(false(),x,y) -> y 0.00/0.16 3: eq(0(),0()) -> true() 0.00/0.16 4: eq(0(),s(x)) -> false() 0.00/0.16 5: eq(s(x),s(y)) -> eq(x,y) 0.00/0.16 6: plus(empty(),x) -> x 0.00/0.16 7: app(x,empty()) -> empty() 0.00/0.16 8: app(x,app(empty(),z)) -> app(empty(),z) 0.00/0.16 9: app(x,plus(y,z)) -> plus(app(x,y),app(x,z)) 0.00/0.16 10: app(x,app(plus(y,z),t)) -> app(plus(app(x,y),app(x,z)),t) 0.00/0.16 11: app(singl(x),singl(y)) -> if(eq(x,y),singl(x),empty()) 0.00/0.16 Number of strict rules: 11 0.00/0.16 Direct POLO(bPol) ... failed. 0.00/0.16 Uncurrying ... failed. 0.00/0.16 Dependency Pairs: 0.00/0.16 #1: #app(x,app(y,z)) ->= #app(app(x,y),z) 0.00/0.16 #2: #app(x,app(y,z)) ->= #app(x,y) 0.00/0.16 #3: #app(x,plus(y,z)) -> #plus(app(x,y),app(x,z)) 0.00/0.16 #4: #app(x,plus(y,z)) -> #app(x,y) 0.00/0.16 #5: #app(x,plus(y,z)) -> #app(x,z) 0.00/0.16 #6: #app(singl(x),singl(y)) -> #if(eq(x,y),singl(x),empty()) 0.00/0.16 #7: #app(singl(x),singl(y)) -> #eq(x,y) 0.00/0.16 #8: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.16 #9: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.16 #10: #app(x,app(plus(y,z),t)) -> #app(plus(app(x,y),app(x,z)),t) 0.00/0.16 #11: #app(x,app(plus(y,z),t)) -> #plus(app(x,y),app(x,z)) 0.00/0.16 #12: #app(x,app(plus(y,z),t)) -> #app(x,y) 0.00/0.16 #13: #app(x,app(plus(y,z),t)) -> #app(x,z) 0.00/0.16 #14: #eq(s(x),s(y)) -> #eq(x,y) 0.00/0.16 Number of SCCs: 3, DPs: 10 0.00/0.16 SCC { #14 } 0.00/0.16 POLO(Sum)... succeeded. 0.00/0.16 s w: x1 + 1 0.00/0.16 #plus w: 0 0.00/0.16 eq w: 0 0.00/0.16 false w: 0 0.00/0.16 true w: 0 0.00/0.16 #eq w: x2 0.00/0.16 if w: 0 0.00/0.16 0 w: 0 0.00/0.16 #app w: 0 0.00/0.16 singl w: 0 0.00/0.16 plus w: 0 0.00/0.16 #if w: 0 0.00/0.16 empty w: 0 0.00/0.16 app w: 0 0.00/0.16 USABLE RULES: { } 0.00/0.16 Removed DPs: #14 0.00/0.16 Number of SCCs: 2, DPs: 9 0.00/0.16 SCC { #8 #9 } 0.00/0.16 only weak rules. 0.00/0.16 Number of SCCs: 1, DPs: 7 0.00/0.16 SCC { #1 #2 #4 #5 #10 #12 #13 } 0.00/0.16 POLO(Sum)... POLO(max)... QLPOS... succeeded. 0.00/0.16 s s: [1] p: 0 0.00/0.16 #plus s: {} p: 0 0.00/0.16 eq s: [2] p: 1 0.00/0.16 false s: [] p: 1 0.00/0.16 true s: [] p: 1 0.00/0.16 #eq s: [2] p: 0 0.00/0.16 if s: [2,3] p: 1 0.00/0.16 0 s: [] p: 0 0.00/0.16 #app s: {1,2} p: 2 0.00/0.16 singl s: 1 0.00/0.16 plus s: {1,2} p: 0 0.00/0.16 #if s: [] p: 0 0.00/0.16 empty s: [] p: 0 0.00/0.16 app s: {1,2} p: 2 0.00/0.16 USABLE RULES: { 1..13 } 0.00/0.16 Removed DPs: #2 #4 #5 #10 #12 #13 0.00/0.16 Number of SCCs: 1, DPs: 1 0.00/0.16 SCC { #1 } 0.00/0.16 only weak rules. 0.00/0.16 Number of SCCs: 0, DPs: 0 0.00/0.16 Next Dependency Pairs: 0.00/0.16 #15: #plus(plus(empty(),x),_1) -> #plus(x,_1) 0.00/0.16 #16: #app(x,app(y,z)) ->= #app(app(x,y),z) 0.00/0.16 #17: #app(x,app(y,z)) ->= #app(x,y) 0.00/0.16 #18: #app(app(x,plus(y,z)),_1) -> #app(plus(app(x,y),app(x,z)),_1) 0.00/0.16 #19: #app(app(singl(x),singl(y)),_1) -> #app(if(eq(x,y),singl(x),empty()),_1) 0.00/0.16 #20: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.16 #21: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.16 #22: #app(app(x,empty()),_1) -> #app(empty(),_1) 0.00/0.16 #23: #app(app(x,app(plus(y,z),t)),_1) -> #app(app(plus(app(x,y),app(x,z)),t),_1) 0.00/0.16 #24: #app(app(x,app(empty(),z)),_1) -> #app(app(empty(),z),_1) 0.00/0.16 Number of SCCs: 2, DPs: 10 0.00/0.16 SCC { #16..19 #22..24 } 0.00/0.16 POLO(Sum)... POLO(max)... QLPOS... succeeded. 0.00/0.16 s s: [1] p: 1 0.00/0.16 #plus s: {} p: 0 0.00/0.16 eq s: [2] p: 2 0.00/0.16 false s: [] p: 2 0.00/0.16 true s: [] p: 2 0.00/0.16 #eq s: [2] p: 0 0.00/0.16 if s: [2,3] p: 1 0.00/0.16 0 s: [] p: 1 0.00/0.16 #app s: {1,2} p: 2 0.00/0.16 singl s: [] p: 0 0.00/0.16 plus s: {1,2} p: 0 0.00/0.16 #if s: [] p: 0 0.00/0.16 empty s: [] p: 0 0.00/0.16 app s: {1,2} p: 2 0.00/0.16 USABLE RULES: { 1..13 } 0.00/0.16 Removed DPs: #17..19 #22..24 0.00/0.16 Number of SCCs: 2, DPs: 4 0.00/0.16 SCC { #16 } 0.00/0.16 only weak rules. 0.00/0.16 Number of SCCs: 1, DPs: 3 0.00/0.16 SCC { #15 #20 #21 } 0.00/0.16 POLO(Sum)... succeeded. 0.00/0.16 s w: 1 0.00/0.16 #plus w: x1 + x2 0.00/0.16 eq w: 1 0.00/0.16 false w: 2 0.00/0.16 true w: 2 0.00/0.16 #eq w: 0 0.00/0.16 if w: x1 + x3 0.00/0.16 0 w: 1 0.00/0.16 #app w: 0 0.00/0.16 singl w: 1 0.00/0.16 plus w: x1 + x2 + 1 0.00/0.16 #if w: 0 0.00/0.16 empty w: 1 0.00/0.16 app w: 2 0.00/0.16 USABLE RULES: { 6 12 } 0.00/0.16 Removed DPs: #15 #21 0.00/0.16 Number of SCCs: 1, DPs: 1 0.00/0.16 SCC { #20 } 0.00/0.16 only weak rules. 0.00/0.16 Number of SCCs: 0, DPs: 0 0.00/0.16 EOF